Consider the equation 221 x 377 y c it is known that

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Question 2.(2+6 points) Consider the equation 221x+ 377y=c. It is known that gcd(221,377) = 13 andthat 13 = (221)(12) + (377)(-7).(a) For which values ofcdoes the equation have an integer solution?
(b) Find all integer solutions for 221x+ 377y= 52.
Keeping Scores:QuestionBonus12345TotalScoreOut of288101514571
Question 3.(5+5 points)(a) It is known thatab(modm) iffa=b+mkfor somekZ. Use thisfact, or the definition of the congruence relation, to prove that ifac(modm) andbd(modm), thenabcd(modm).

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