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Provisory Pairs (Posted on 2023-01-21)

Determine all possible pairs of positive integers satisfying each of these conditions:

The last digit of their sum is 5.
Their difference is a prime number.
Their product is a perfect square.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

There seems to be an uncountable number of pairs satisfying the given conditions.
Larry has posited (without proof) that IF the sum of a pair ends in 5 AND their product is a square THEN not only is their difference a prime, but also a prime ending in 3 or 7, and he has also listed some of the valid pairs in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution and Pattern without proof	Larry	2023-01-21 11:00:28
some numbers to look at	Charlie	2023-01-21 09:11:18

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