Let n and (n+1) be the integers.

n

n

2n

2(n

This equation has no integer solution for n. If n is an integer, n

There are no such integers.

n

^{2}+ (n+1)^{2}= 340n

^{2}+ n^{2}+ 2n + 1 = 3402n

^{2}+ 2n = 339 (subtract 1 from both sides of the equation, collect terms)2(n

^{2}+n) = 339 (factor out 2 for clarity)This equation has no integer solution for n. If n is an integer, n

^{2}is an integer and (n^{2}+n) is an integer. No integer exists such that multiplying it by 2 will give 339.There are no such integers.