Prove that any number of the form pq, where p and q are prime numbers greater than 2, can be written as the difference of two squares in exactly two distinct ways.
If we want to prove it, we need to prove every odd number can be expressed as the difference of two squares, which is very easy.
Suppose this odd number to be 2n-1, then we can see 2n-1=n2-(n-1)2
Then we let pq=a2-b2=(a-b)(a+b).Then we can see either p=a-b & q=a+b or 1=a-b & pq=a+b, which are two different forms of squares.
SL
Related STEP University answers
All answers ▸Let p and q be different primes greater than 2. Prove that pq can be written as difference of two squares in exactly two different ways.
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