Simplify the following congruence: $$−169 \equiv \text{ ?} \mod 52 $$ (By simplify, we mean find the smallest non-negative whole number which is congruent to $-169$ modulo $52$.)
Simplify the following congruence:
$$−501 \equiv \text { ?} \mod 213$$ (By simplify, we mean find the smallest non-negative whole number which is congruent to $-501$ modulo $213$.)