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Old 2020-03-20, 15:16   #2
xilman
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Quote:
Originally Posted by enzocreti View Post
216=3^2*(182^2-331*10^2)


is there any other positive cube that can be written as


a^2*(b^2-r*10^2)?


with a and b positive and coprime, r prime?
Since d^3 = d^2 * d, all you are asking is whether d = (b^2 - 100r) is positive. In other words, for what values of b and r is b^2 > 100r and b is co-prime to d..

It should now be obvious that there are an infinite number of solutions. Picking just one pretty much at random, let r =1. In that case b^2 > 100, or b> 10. One such value is 11. Plugging in the numbers, d=121-100 = 21.

Indeed 21^3 = 9261 = 441 * (11^2 - 10 * 1^2).

Why do you post questions which are so trivial to answer with even the slightest amount of thought?

Last fiddled with by xilman on 2020-03-20 at 15:20
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