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Some Primes Differ by a Square (Posted on 2023-05-31)

Determine all possible pairs (p, q) of prime numbers that satisfy this set of simultaneous equations:

p - q = a²
p*q - q = b²

where each of a and b is a positive integer.

Validate your answer by providing sufficient analytic reasoning.

See The Solution Submitted by K Sengupta

Rating: 4.5000 (2 votes)

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re: Solution

Comment 2 of 2 |

(In reply to Solution by H M)

If p-1!=q, then it is not necessarily true that p-1=q^n. Case 2 should say that p-1=qn^2 for some integer n. Does anybody know a correct proof for this case?

Posted by Math Man on 2023-07-01 21:02:02

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