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Printsmc
number theory senior
Problem
For natural numbers, when is divided by , the quotient is and the remainder is . When is divided by , the quotient is and the remainder is . Then, when is divided by , the remainder is:
(A)
(B)
(C)
(D)
Solution
We are given and . Plugging the second equation into the first yields: If we divide by , the quotient would be , and the remainder would be , which is option .
Final answer
A