Question

Determinati numerele abc in baza zece care verifica relatia ab in baza zece x(b^2+c^2)=2014

Answer 1

l) 2014=38x53=53x38
Avem doua cazuri:
1) ab=38 => a=3 si b=8
b^2+c^2=53 <=> 64+c^2=53 imposibil (c=cifra)
2) ab=53 => a=5 si b=3
b^2+c^2=38 <=> 9+c^2=38 <=> c^2=29 imposibil (c^2 tb sa fie patrat perfect)
ll) 2014=19x106
ab=19 => a=1 si b=9
b^2+c^2=106 <=> 81+c^2=106 <=> c^2=25 => c=5
abc=195

Verificare: 19x(81+25)=19x106=2014