南京大学孙智伟教授主页上的一些悬赏问题

cooooldog

可以从二维码看链接; 估计对中国民间科学家的力量太过于恐惧
孙教授只用英文形式给出悬赏,而且单位应该是美元(数学家太不严谨了, 好多国家的元都是用$, 美元就应该用USD)




My paper Further Results on Hilbert's Tenth Problem (based on my PhD thesis in 1992)

My 24-Conjecture with $2400 Prize (see also OEIS A281976 and arXiv:1701.05868）

　　 Any natural number n can be written as the sum of squares of four nonnegative integers x, y, z and w such that both x and x+24y are squares. [This has been verified for n up to 1010 by Qing-Hu Hou.]

My 1-3-5 Conjecture with $1350 Prize (see also OEIS A271518 and arXiv:1604.06723）

　　 Any natural number n can be written as the sum of squares of four nonnegative integers x, y, z and w such that x+3y+5z is also a square. [This has been verified for n up to 1010 by Qing-Hu Hou.]

My Conjecture involving Primes and Powers of 2 with $1000 Prize (see also Conjecture 3.6(i) of this paper)

　　 Every n = 2, 3, ... can be written as a sum of two positive integers k and m such that 2k + m is prime. [This has been verified for n up to 107.]

My Conjecture on Unit Fractions involving Primes with $500 Prize (see also Conjecture 4.1(i)-(ii) of this paper)

　　 Let d be -1 or 1. Each positive rational number can be written as 1/(p(1)+d) + 1/(p(2)+d) + ... + 1/(p(k)+d), where p(1),...,p(k) are distinct primes.

My Conjecture on Primes of the Form x2+ny2 with $200 Prize (see also Conjecture 2.21(i) of this paper)

　　 Each n = 2,3,... can be written as x+y with x and y positive integers such that x+ny and x2+ny2 are both prime.

My Conjecture related to Bertrand's Postulate with $100 Prize (see also Conjecture 2.18 of this paper)

　　 Let n be any positive integer. Then, for some k=0,...n, both n+k and n+k2 are prime. [I have verified this conjecture for n up to 200,000,000.]

My 100 Conjectures on Representations involving Primes or related Things

My Little 1-3-5 Conjecture with $135 Prize (see this paper for more such conjectures)

　　 Each n = 0,1,2,... can be written as x(x+1)/2+y(3y+1)/2+z(5z+1)/2 with x,y,z nonnegative integers. [I have proved the weaker version with x,y,z integers.]

My 60 Open Problems on Combinatorial Properties of Primes

cooooldog

这里有很多数论问题,估计研究数论的会感兴趣