Assume gcd(a,b) = 1. Show that if a and b are positive integers, and if ab is a square, then a and b are also squares. Hint: use order function of unique facorization Any ideas?
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When you factor a square, each prime must occur to an even power. If a,b are coprime, then they share no prime factors. So if their product has only even prime powers, and each prime came only from a or only from b, what can you conclude?
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