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# Number Theory

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If 3x+7=2 (mod 16), then 2x+11+4x is congruent (mod 16) to what integer between 0 and 15, inclusive?

May 14, 2022

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$$3x + 7 \equiv 2 \pmod{16}\\ 3x \equiv -5 \pmod{16}\\ 33x \equiv -55 \pmod{16}\\ x \equiv 9 \pmod{16}$$

Now you just take x = 9, then calculate the value of 2x + 11 + 4x. The answer is the remainder when 2x + 11 + 4x is divided by 16.

May 14, 2022