Strange

Number Theory Level pending

What is the smallest two digit square whose digits are squares and has the property that the sum and difference of its digits are both primes ?


The answer is 49.

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2 solutions

Gini Mas
May 21, 2016

If each digit is a square, that two digit number must have digits from the numbers 1, 4 or 9 (the single digit perfect squares) with replacement. As such, we can write out these possible numbers as 11, 14, 19, 41, 44, 49, 91, 94 and 99 (3 x 3 numbers). The only square in that list is 49, and it happens to have the property of having a prime sum and difference in its digits.

Jon Sy
May 8, 2016

Hello There are only 6 perfect squares. Thus, a viable method to solve this problem is by method guess and check . By guess and check we find the answer is 49 \boxed{49} . (Er dumb)Extension: Do there exist any other perfect squares such that any 2 consecutive of its perfect square digits sum to a prime? (For example, 49 because the only pair of consecutive digits here is 49, and 9-4=5 and 4+9 = 13) Thank

i AGREEE BAD PROBLEM

Percy 17 hax0r - 5 years ago

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