Find all 2 digit base 10 integer pairs (X, Y) such that:
- Y is not larger than X
- (sod(X*Y))^3 equals (sod(X))^2 + (sod(Y))^2
... where sod(n) indicates the sum of digits of n
I found only (73,14) the product is 1022 and 5^2=10^2+5^2
Method: find cubes that are the sum of two squares up to 18^2
5^3=2^2+11^2
2^3=2^2+2^2
5^3=10^2+5^2
The first gives a small list of sod=11 to multiply by 11 or 20. None give a number with sod=5
The second is only 11*11, 11*20, 20*20, none gives sod=5
The last has the most pairs of numbers to try but I only found the one solution.
edit: I forgot to check 50 and as a result missed
(28,50)
(46,50)
(62,50)
(82,50)
Edited on November 20, 2019, 3:03 pm
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Posted by Jer
on 2019-11-20 13:12:58 |
solution?
