Question

Which integers between -10 and 10 can be expressed as the difference of two squares? Which cannot?

Answer 1

Answer:

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Answer 2

Answer:

3 is not the only odd number which is prime. Quite a few of the odds are prime: 3, 5, 7, 11, 13, 17, 19 and so on. Consequently, quite a few differences between squares are primes:

9–4=5 (prime)

16–9=7 (prime)

and so on.

I have only considered the difference between squares of consecutive numbers in this example, but of course, there are many other pairs of numbers: in some cases, the difference will be prime and in others not.