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SOD cubed equals Sum of Squares of SODs (Posted on 2019-11-20) Difficulty: 3 of 5
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

See The Solution Submitted by Larry    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
solution? | Comment 1 of 4
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
  Posted by Jer on 2019-11-20 13:12:58

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