Congruence!

Number Theory Level 2

$\large 29x+27 \equiv 6x+51\pmod5$

Find all integers $x$ that satisfy the linear congruence above

Each $x$ can be written as $x \equiv a \pmod b$ , where $a$ and $b$ are positive integers satisfying $0 \leq a < b$ . Submit your answer as $a+b$ .

1 solution

Tommy Li
Jun 18, 2016

$29x+27 \equiv 6x+51 \pmod{5}$

$23x \equiv 24 \pmod{5}$

$3x \equiv 4 \pmod{5}$

$x \equiv \frac{4+5}{3} \pmod{5}$

$x \equiv 3 \pmod{5}$

$a+b = 3+5 = 8$