N is a positive integer less than 2015.

Find all values of N such that:
N is equal to precisely 36 less than the square of the sum of digits of N.

***As an extra challenge, solve this puzzle without using a computer program assisted method.

solved analytically for 2-digit N=1Oa+b:

(a+b)^2-36=1Oa+b

a^2+(2b-10)*a+b^2-b=0

getting a=6 if b=4   and a=4 if b=5 

64=(6+4)^2-36     and

45=(4+5)^2-36

did not try for larger numbers, involving 3 unknowns-

leave it to others.

Posted by Ady TZIDON on 2015-01-20 17:15:54