For which positive integers n do there exist integers x and y such with (x, n) = 1, (y, n) = 1, such that?
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For which positive integers n do there exist integers x and y such with (x, n) = 1, (y, n) = 1, such that
It is easy to see that n = 2 satifies the given congruence. If n is odd, every prime p dividing n should satisfy.
The answer given in the book is:where
= 0 or 1, the primes p in the product are all
, and
.
How do they get thein the product?