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A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Relative Powers

Stage: 4 Short Challenge Level: Challenge Level:1
See all short problems arranged by curriculum topic in the short problems collection

The square of a number is 12 more than the number itself. The cube of the number is 9 times the number. What is the number?

 

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

This problem is taken from the UKMT Mathematical Challenges.