Question

Determinati toate nr. prime xy care verifica relatia: 0,X(Y) - 0,Y(X)= 0,0(1)x16

Answer 1

$\sf 0,x(y)-0,y(x)=0,0(1)*16 \\ \\ \frac{\overline{xy}-x}{90}- \frac{\overline{yx}-y}{90}=16* \frac{1}{90}|*90 \\ \\ 10x+y-x-10y-x+y=16 \\ \\ 8x-8y=16|:8 \\ \\ x-y=2 \\ \\ Pentru~x=5 \longrightarrow y=3 \\ \\ Pentru~x=7 \longrightarrow y=5 \\ \\ \boxed{\sf Numerele:53;~75}$