So i just got a hang of congruence but I am unable to solve this also how does one find all integers solution for $1566x - 232y = 116$ such that $0 \leq x,y \leq 100$
2026-03-27 10:08:56.1774606136
Proving that there is no integer solution to $3996x-3071y=-482$
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$$ (3996,3071)=37$$ which does not divide $$482$$
$$108x-83y=\dfrac{482}{37}$$
The left hand side is an integer unlike the right hand side.
As $(1566,232,116)=58$
$$1566x-232y=116\iff27x-4y=2 \iff 27(x-2)=4(y-13)\iff y-13=\dfrac{27(x-2)}4$$
As $(27,4)=1,4|(x-2)\iff x=4m+2$ where $m$ is any integer
Consequently, $y-13=\dfrac{27(x-2)}4=?$