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Find the pairs (Posted on 2020-10-13)

Determine the natural numbers m,n such as 85^m-n⁴=4.

No Solution Yet Submitted by Danish Ahmed Khan

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I found only one

| Comment 1 of 22

One solution is (m,n) = (1, 3)

85^1 - 3^4 = 85 - 81 = 4

I have not proved it is unique, but when I tested in the program below up to 1000, I found only the one answer.

big = 1000

for m in range(1,big):
    for n in range(1,big):
        if 85**m - n**4 == 4:
            print(m,n)

Edited on October 13, 2020, 10:24 am

Posted by Larry on 2020-10-13 10:21:32

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