修改一下一个重要概念（原稿不严谨，修改一下更准确）：
原稿：n次相邻数：开n次方（n大于等于2）的方根的整数部分相等（或差1）的俩或多个整数，叫n次相邻数。
修改为：
n次相邻数：设a为整数的n次方根的整数部分，差小于（a+1）^n-a^n的俩或多个整数（其中n大于等于2） ，称为n次相邻数。
a=6859 b=4913 x=11772 a^(1/3)=19 b^(1/3)=17 x^(1/3)=22
这一组数据 ，虽然没有公因子，但同除以2*2*2=8后就得到一组3次相邻数，分别是857，614和1471（取整数部分），857^(1/3)=9，614^(1/3)=8（取整数部分，是3次相邻数），1471^(1/3)=11.
可以证明这是一个定理：若a，b，x=a+b这三个数同除以r的3次方（小于等于其中的最小的一个）所得商的整数部分是一组3次相邻数，则a，b和x之中必有至少一个为非3，4，5，6，……，n次方数
857-614=243<1000-9*9*9=1000-729=271.
通过以上数据可以看出来，a，b和a+b之中总有两个（或者除以一个公因子或不是公因子的r的3，4，5，……n次方）是3，4，5，……，n次相邻数（这需要严格证明的），所以，a，b和a+b三者不会同时为3，4，5，6，……，n次方数。所以，费马方程的解只能在勾股数中找了，勾股数中没有就没有了。
a1=100 s=54
a=1 b=4 x=5 a^(1/3)=1 p^(1/3)=2 q^(1/3)=2.57128159065824
a=1 b=32 x=33 a^(1/3)=1 p^(1/3)=4 q^(1/3)=10.0826483760905
a=2 b=16 x=18 a^(1/3)=1.25992104989487 p^(1/3)=4 q^(1/3)=6.38250429885991
a=2 b=54 x=56 a^(1/3)=1.25992104989487 p^(1/3)=6 q^(1/3)=14.29313899763
a=3 b=36 x=39 a^(1/3)=1.44224957030741 p^(1/3)=6 q^(1/3)=10.9279031465542
a=4 b=1 x=5 a^(1/3)=1.5874010519682 p^(1/3)=2 q^(1/3)=2.57128159065824
a=4 b=8 x=12 a^(1/3)=1.5874010519682 p^(1/3)=4 q^(1/3)=4.30886938006377
a=4 b=27 x=31 a^(1/3)=1.5874010519682 p^(1/3)=6 q^(1/3)=9.06536770125941
a=4 b=64 x=68 a^(1/3)=1.5874010519682 p^(1/3)=8 q^(1/3)=16.0208062653131
a=5 b=100 x=105 a^(1/3)=1.7099759466767 p^(1/3)=10 q^(1/3)=21.5622855821288
a=6 b=18 x=24 a^(1/3)=1.81712059283214 p^(1/3)=6 q^(1/3)=7.11378660898013
a=8 b=4 x=12 a^(1/3)=2 p^(1/3)=4 q^(1/3)=4.30886938006377
a=8 b=32 x=40 a^(1/3)=2 p^(1/3)=8 q^(1/3)=10.2851263626329
a=9 b=12 x=21 a^(1/3)=2.0800838230519 p^(1/3)=6 q^(1/3)=6.0822019955734
a=9 b=96 x=105 a^(1/3)=2.0800838230519 p^(1/3)=12 q^(1/3)=21.0271757016239
a=10 b=50 x=60 a^(1/3)=2.15443469003188 p^(1/3)=10 q^(1/3)=13.7506886707414
a=12 b=9 x=21 a^(1/3)=2.28942848510666 p^(1/3)=6 q^(1/3)=6.0822019955734
a=12 b=72 x=84 a^(1/3)=2.28942848510666 p^(1/3)=12 q^(1/3)=17.4657834825919
a=14 b=98 x=112 a^(1/3)=2.41014226417523 p^(1/3)=14 q^(1/3)=21.3997496113016
a=16 b=2 x=18 a^(1/3)=2.51984209978975 p^(1/3)=4 q^(1/3)=6.38250429885991
a=16 b=54 x=70 a^(1/3)=2.51984209978975 p^(1/3)=12 q^(1/3)=14.6930196547085
a=18 b=6 x=24 a^(1/3)=2.6207413942089 p^(1/3)=6 q^(1/3)=7.11378660898013
a=18 b=48 x=66 a^(1/3)=2.6207413942089 p^(1/3)=12 q^(1/3)=13.7998739749046
a=20 b=25 x=45 a^(1/3)=2.71441761659491 p^(1/3)=10 q^(1/3)=10.0826483760905
a=24 b=36 x=60 a^(1/3)=2.88449914061482 p^(1/3)=12 q^(1/3)=12.3244802954981
a=25 b=20 x=45 a^(1/3)=2.92401773821287 p^(1/3)=10 q^(1/3)=10.0826483760905
a=27 b=4 x=31 a^(1/3)=3 p^(1/3)=6 q^(1/3)=9.06536770125941
a=27 b=32 x=59 a^(1/3)=3 p^(1/3)=12 q^(1/3)=12.0575935104481
a=28 b=49 x=77 a^(1/3)=3.03658897187566 p^(1/3)=14 q^(1/3)=14.7130647268414
a=32 b=1 x=33 a^(1/3)=3.1748021039364 p^(1/3)=4 q^(1/3)=10.0826483760905
a=32 b=8 x=40 a^(1/3)=3.1748021039364 p^(1/3)=8 q^(1/3)=10.2851263626329
a=32 b=27 x=59 a^(1/3)=3.1748021039364 p^(1/3)=12 q^(1/3)=12.0575935104481
a=32 b=64 x=96 a^(1/3)=3.1748021039364 p^(1/3)=16 q^(1/3)=17.2354775202551
a=36 b=3 x=39 a^(1/3)=3.30192724889463 p^(1/3)=6 q^(1/3)=10.9279031465542
a=36 b=24 x=60 a^(1/3)=3.30192724889463 p^(1/3)=12 q^(1/3)=12.3244802954981
a=36 b=81 x=117 a^(1/3)=3.30192724889463 p^(1/3)=18 q^(1/3)=19.88011616243
a=40 b=100 x=140 a^(1/3)=3.41995189335339 p^(1/3)=20 q^(1/3)=22.637023919259
a=48 b=18 x=66 a^(1/3)=3.63424118566428 p^(1/3)=12 q^(1/3)=13.7998739749046
a=49 b=28 x=77 a^(1/3)=3.65930571002297 p^(1/3)=14 q^(1/3)=14.7130647268414
a=50 b=10 x=60 a^(1/3)=3.68403149864039 p^(1/3)=10 q^(1/3)=13.7506886707414
a=50 b=80 x=130 a^(1/3)=3.68403149864039 p^(1/3)=20 q^(1/3)=20.7235109805926
a=54 b=2 x=56 a^(1/3)=3.77976314968462 p^(1/3)=6 q^(1/3)=14.29313899763
a=54 b=16 x=70 a^(1/3)=3.77976314968462 p^(1/3)=12 q^(1/3)=14.6930196547085
a=64 b=4 x=68 a^(1/3)=4 p^(1/3)=8 q^(1/3)=16.0208062653131
a=64 b=32 x=96 a^(1/3)=4 p^(1/3)=16 q^(1/3)=17.2354775202551
a=72 b=12 x=84 a^(1/3)=4.16016764610381 p^(1/3)=12 q^(1/3)=17.4657834825919
a=72 b=96 x=168 a^(1/3)=4.16016764610381 p^(1/3)=24 q^(1/3)=24.3288079822936
a=80 b=50 x=130 a^(1/3)=4.30886938006377 p^(1/3)=20 q^(1/3)=20.7235109805926
a=81 b=36 x=117 a^(1/3)=4.32674871092222 p^(1/3)=18 q^(1/3)=19.88011616243
a=96 b=9 x=105 a^(1/3)=4.57885697021333 p^(1/3)=12 q^(1/3)=21.0271757016239
a=96 b=72 x=168 a^(1/3)=4.57885697021333 p^(1/3)=24 q^(1/3)=24.3288079822936
a=98 b=14 x=112 a^(1/3)=4.61043629205845 p^(1/3)=14 q^(1/3)=21.3997496113016
a=100 b=5 x=105 a^(1/3)=4.64158883361278 p^(1/3)=10 q^(1/3)=21.5622855821288
a=100 b=40 x=140 a^(1/3)=4.64158883361278 p^(1/3)=20 q^(1/3)=22.637023919259
其中p2ab，q=a^2+b^2，x=a+b，可见p和q不能同时开立方。
代码如下：
Private Sub Command1_Click()
Dim a, b
a1 = Val(Text1)
a = 1
Do While a <= a1
b = 1
Do While b <= a1
x = a + b
y = b
z = a
p = 2 * b * a
q = a ^ 2 + b ^ 2
X1 = x ^ (1 / 3): Y1 = Abs(y) ^ (1 / 3): z1 = z ^ (1 / 3): p1 = p ^ (1 / 3): q1 = q ^ (1 / 3)
Print p1
If InStr(p1, ".") = 0 And a <> b Then
s = s + 1
s1 = s1 & "a=" & a & " b=" & b & " x=" & x & " a^(1/3)=" & z1 & " p^(1/3)=" & p1 & " q^(1/3)=" & q1 & vbCrLf
Else
s = s
End If
b = b + 1
Loop
a = a + 1
Loop
If s > 0 Then
Text2 = "a1=" & a1 & " s=" & s & vbCrLf & s1
Else
Text2 = "wu jie"
End If
End Sub
Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Me.Cls
End Sub
a1=100 s=22
a=2 b=11 x=13 a^(1/3)=1.25992104989487 p^(1/3)=3.53034833532606 q^(1/3)=5
a=5 b=10 x=15 a^(1/3)=1.7099759466767 p^(1/3)=4.64158883361278 q^(1/3)=5
a=9 b=46 x=55 a^(1/3)=2.0800838230519 p^(1/3)=9.39024187300355 q^(1/3)=13
a=10 b=5 x=15 a^(1/3)=2.15443469003188 p^(1/3)=4.64158883361278 q^(1/3)=5
a=10 b=30 x=40 a^(1/3)=2.15443469003188 p^(1/3)=8.43432665301749 q^(1/3)=10
a=11 b=2 x=13 a^(1/3)=2.22398009056932 p^(1/3)=3.53034833532606 q^(1/3)=5
a=16 b=88 x=104 a^(1/3)=2.51984209978975 p^(1/3)=14.1213933413043 q^(1/3)=20
a=17 b=68 x=85 a^(1/3)=2.57128159065824 p^(1/3)=13.2229780369159 q^(1/3)=17
a=18 b=26 x=44 a^(1/3)=2.6207413942089 p^(1/3)=9.78194649301749 q^(1/3)=10
a=26 b=18 x=44 a^(1/3)=2.96249606840737 p^(1/3)=9.78194649301749 q^(1/3)=10
a=26 b=39 x=65 a^(1/3)=2.96249606840737 p^(1/3)=12.6577345461767 q^(1/3)=13
a=30 b=10 x=40 a^(1/3)=3.10723250595386 p^(1/3)=8.43432665301749 q^(1/3)=10
a=39 b=26 x=65 a^(1/3)=3.39121144301417 p^(1/3)=12.6577345461767 q^(1/3)=13
a=40 b=80 x=120 a^(1/3)=3.41995189335339 p^(1/3)=18.5663553344511 q^(1/3)=20
a=46 b=9 x=55 a^(1/3)=3.58304787101595 p^(1/3)=9.39024187300355 q^(1/3)=13
a=47 b=52 x=99 a^(1/3)=3.60882608013869 p^(1/3)=16.9711158883629 q^(1/3)=17
a=52 b=47 x=99 a^(1/3)=3.73251115681725 p^(1/3)=16.9711158883629 q^(1/3)=17
a=68 b=17 x=85 a^(1/3)=4.08165510191735 p^(1/3)=13.2229780369159 q^(1/3)=17
a=75 b=100 x=175 a^(1/3)=4.21716332650875 p^(1/3)=24.6621207433047 q^(1/3)=25
a=80 b=40 x=120 a^(1/3)=4.30886938006377 p^(1/3)=18.5663553344511 q^(1/3)=20
a=88 b=16 x=104 a^(1/3)=4.44796018113863 p^(1/3)=14.1213933413043 q^(1/3)=20
a=100 b=75 x=175 a^(1/3)=4.64158883361278 p^(1/3)=24.6621207433047 q^(1/3)=25
其中p2ab，q=a^2+b^2，x=a+b，可见p和q不能同时开立方。
代码如下：
Private Sub Command1_Click()
Dim a, b
a1 = Val(Text1)
a = 1
Do While a <= a1
b = 1
Do While b <= a1
x = a + b
y = b
z = a
p = 2 * b * a
q = a ^ 2 + b ^ 2
X1 = x ^ (1 / 3): Y1 = Abs(y) ^ (1 / 3): z1 = z ^ (1 / 3): p1 = p ^ (1 / 3): q1 = q ^ (1 / 3)
Print q1
If InStr(q1, ".") = 0 And a <> b Then
s = s + 1
s1 = s1 & "a=" & a & " b=" & b & " x=" & x & " a^(1/3)=" & z1 & " p^(1/3)=" & p1 & " q^(1/3)=" & q1 & vbCrLf
Else
s = s
End If
b = b + 1
Loop
a = a + 1
Loop
If s > 0 Then
Text2 = "a1=" & a1 & " s=" & s & vbCrLf & s1
Else
Text2 = "wu jie"
End If
End Sub
Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Me.Cls
End Sub
a1=100 s=8
a=7 b=24 x=31 a^(1/4)=1.62657656169779 p^(1/4)=4.28139028585615 q^(1/4)=5
a=15 b=20 x=35 a^(1/4)=1.96798967126543 p^(1/4)=4.94923200383977 q^(1/4)=5
a=20 b=15 x=35 a^(1/4)=2.11474252688113 p^(1/4)=4.94923200383977 q^(1/4)=5
a=24 b=7 x=31 a^(1/4)=2.21336383940064 p^(1/4)=4.28139028585615 q^(1/4)=5
a=28 b=96 x=124 a^(1/4)=2.30032663379121 p^(1/4)=8.56278057171229 q^(1/4)=10
a=60 b=80 x=140 a^(1/4)=2.78315768371374 p^(1/4)=9.89846400767953 q^(1/4)=10
a=80 b=60 x=140 a^(1/4)=2.99069756244244 p^(1/4)=9.89846400767953 q^(1/4)=10
a=96 b=28 x=124 a^(1/4)=3.13016916014657 p^(1/4)=8.56278057171229 q^(1/4)=10
其中p2ab，q=a^2+b^2，x=a+b，可见p和q不能同时开4次方
代码如下：
Private Sub Command1_Click()
Dim a, b
a1 = Val(Text1)
a = 1
Do While a <= a1
b = 1
Do While b <= a1
x = a + b
y = b
z = a
p = 2 * b * a
q = a ^ 2 + b ^ 2
X1 = x ^ (1 / 4): Y1 = Abs(y) ^ (1 / 4): z1 = z ^ (1 / 4): p1 = p ^ (1 / 4): q1 = q ^ (1 / 4)
Print q1
If InStr(q1, ".") = 0 And a <> b Then
s = s + 1
s1 = s1 & "a=" & a & " b=" & b & " x=" & x & " a^(1/4)=" & z1 & " p^(1/4)=" & p1 & " q^(1/4)=" & q1 & vbCrLf
Else
s = s
End If
b = b + 1
Loop
a = a + 1
Loop
If s > 0 Then
Text2 = "a1=" & a1 & " s=" & s & vbCrLf & s1
Else
Text2 = "wu jie"
End If
End Sub
Private Sub Command2_Click()
Text1 = ""
Text2 = ""
Me.Cls
End Sub