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Omni-MATH / At a recent math contest, Evan was asked to find 2^{2016}(bmod p) for a given prime number p with 100<p<500. Evan has forgotten what the prime p was, but still remembers how he sol…

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problem

At a recent math contest, Evan was asked to find $2^{2016}(\bmod p)$ for a given prime number pp with 100<p<500100<p<500. Evan has forgotten what the prime pp was, but still remembers how he solved it: - Evan first tried taking 2016 modulo p−1p-1, but got a value ee larger than 100. - However, Evan noted that e−12(p−1)=21e-\frac{1}{2}(p-1)=21, and then realized the answer was $-2^{21}(\bmod p)$. What was the prime pp?
Plain-text mathematical notation (without MathML)
At a recent math contest, Evan was asked to find $2^{2016}(\bmod p)$ for a given prime number p with 100<p<500. Evan has forgotten what the prime p was, but still remembers how he solved it: - Evan first tried taking 2016 modulo p−1, but got a value e larger than 100. - However, Evan noted that e−(1)/(2)(p−1)=21, and then realized the answer was $-2^{21}(\bmod p)$. What was the prime p?
Original LaTeX notation
At a recent math contest, Evan was asked to find $2^{2016}(\bmod p)$ for a given prime number $p$ with $100<p<500$. Evan has forgotten what the prime $p$ was, but still remembers how he solved it: - Evan first tried taking 2016 modulo $p-1$, but got a value $e$ larger than 100. - However, Evan noted that $e-\frac{1}{2}(p-1)=21$, and then realized the answer was $-2^{21}(\bmod p)$. What was the prime $p$?

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Source and history

task_id
0872e0f0-0789-5967-8136-c252fdbe84e8
task_key
test--0872e0f0-0789-5967-8136-c252fdbe84e8
task_revision_id
1
config / split
/ test

Official source

initial import