I am trying to find all integer solutions to the modular congruence $5x^7+x^2+2x \equiv 2\pmod {28}$
I broke it up into 2 cases: that is $\pmod 2,\pmod 7$.
Using the laws of congruence and Fermat's Little Theorem I got:
$5x^7+x^2+2x \equiv x\equiv1\pmod 2$
and
$5x^7+x^2+2x \equiv x^2+7x\pmod 2$
but I am not sure how to use this result I got. Can anyone help please?