Obviously true, right?

Number Theory Level 3

True or False?

There exists integers x , y x,y so that for all non-negative integer n n , x n − y n = 1 x^n-y^n=1 .

True False

Steven Jim by Steven Jim , 17, Vietnam

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2 solutions

Aaghaz Mahajan
Jan 16, 2018

0 is a non negative integer. Putting n as 0 will make LHS equal to 0 for any pair of integers x and y.

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Steven Jim
Jan 16, 2018

Assume that the answer is true. Then x − y = 1 x-y=1 and x 2 − y 2 = 1 x^2-y^2=1 , or x = 1 x=1 and y = 0 y=0 . In this case, though, x 0 − y 0 x^0-y^0 is undefined. Thus the answer must be false.

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