Impossible Unit Digit

Number Theory Level 1

$\color{#3D99F6} x$ is a positive integer, so is $\color{#3D99F6} 5x+31$ .

Which cannot appear as unit digit of $\color{#3D99F6} 5x+31$ ?

Dessert :

Generalize this for $\color{#20A900} ax+b$ replacing $\color{#3D99F6} 5x+31$ ( $\color{#3D99F6} a$ , $\color{#3D99F6} b$ and $\color{#3D99F6} x$ are positive integers).

1 7 6

1 solution

Muhammad Rasel Parvej
Jan 2, 2018

$5x+31$ and $5x+1$ has same unit digit.

But the unit digit of $5x$ is either $0$ or $5$ .

So, the unit digit of $5x+31$ is either $1$ or $6$ .

Hence the answer is $\boxed{7}$ .