Question

Determinati numerele ab in baza zece astfel incat B= ab in baza zece +5ba in baza zece - 126 sa fie patrat perfect

Answer 1

ab+5ba-126 ==
=10a+b+500+10b+a-126=
=11*(a+b)+374=
=11*(a+b)+11*34=
=11*(a+b+34)
  a+b+34=11*11*x^2=(11*x)^2 
1≤a≤9 , 1≤b≤9  ⇒ 2≤a+b≤18 ⇒  2+34≤a+b+34≤18+34
 36≤a+b+34≤52 ⇒ 36≤11*k^2≤52 rezulta k^2=4 deci k=2 
a+b+34=11*4=44 rezulta a+b=10
numerele  ab sunt 19,28,37,46,55,64,73,82,91