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第 37届普特南数学竞赛 (美国 )中一题为 :求不定方程 |pr- qs|=1的整数解 ,其中 p,q为素数 ,r,s是大于1的正整数 ,并证明你所得到的是全部解 .借助于费马数的非方幂性[1 ] 可给出原题的一个新解法 .解 不妨设 prqs,方程化为 pr- qs=1 ,又 p,q不能全为奇数 ,故 p,q之一等于 2
The first question in the 37th Putnam Mathematics Contest (USA) is: Find the integer solution of the indefinite equation |pr-qs|=1, where p,q is a prime number and r,s is a positive integer greater than 1 and proves that you All the solutions are obtained. With the aid of the non-square exponent of the Fermat Number [1], a new solution to the original problem can be given. The solution may be prqs, the equation is pr-qs=1, and p, q cannot be complete. Odd number, so one of p,q is equal to 2