a(X)

Number Theory Level pending

Let $a(x)$ be a function on 2-digit numbers such that $a(23)=13, a(45)=41,a(61)=37.$

If $a(a(x))=1$ , find x.

71 45 68 no answer

1 solution

Iancarlo Espinosa
Aug 6, 2014

if x = ab (a,b digits) => a(x) = a^2 + b^2
a(23) = 4 + 9 = 13
a(45) = 16+25 = 41
a(61) = 36 + 1 = 37
a(a(x)) = 1+0+0+......+0 =>
a(x) = 10^n
68 = 36 + 64 = 100 = 10^2 =>
x=68

correct :)

math man - 6 years, 10 months ago

$a(x)$ is still a function. It may not be a linear nor a polynomial function, but it is still a function of $x$ .

Why can't x be 86, or 13?

Calvin Lin Staff - 6 years, 8 months ago

a(X)

1 solution

0 pending reports