Question

Determinati nr nat de forma ab( in baza 10) , stiind ca suma dintre ab( in b 10) si ba( in baza 10) este patrat perfect

Answer 1

ab=10a+b
ba=10b+a

ab+ba=10a+b+10b+a
ab+ba=11a+11b=11(a+b)
Ca sa fie patrat perfect, a+b=11
=>a=2, b=9
=>a=3, b=8
=>a=4, b=7
=>a=5, b=6
=>a=6, b=5
=>a=7, b=4
=>a=8, b=3
=>a=9, b=2