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A Pythagorean piglet (Posted on 2012-09-22) Difficulty: 3 of 5

Finding solutions to x2- b2=b2-1 is a bit too easy these days, so let b itself be the multiple of a square, say, yz2

For both y>1 and z>1, prove that y is not a square, or find a counter-example.

See The Solution Submitted by broll    
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Solution Oinking solution. | Comment 1 of 4
You want b = yz^2 where y is not a square, but if y were a square, say y = a^2 then you'd have b= a^2*z^2 = (az)^2 which is a square not the multiple of a square as sought.

This proves that y cannot be a square, so there will be no counterexamples.  Now to find if any solutions actually exist.

I found the first 3 values of b (5, 29, 169) and put them in OEIS which returned
The sequence contains 195025 which is 7801*5^2

  Posted by Jer on 2012-09-25 16:17:25
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