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Basic Applications of Modular Arithmetic
Solve integer equations, determine remainders of powers, and much more with the power of Modular Arithmetic.
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There are \(81\) groups of \(21\) students. When we regroup all of the students so that each group has \(5\) members, how many students will be left without a group?
Excel in math and science
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by Brilliant Staff
John and Amy have \(48\) and \(51\) quarters, respectively. If they combine all of their quarters and change as much as possible into dollar bills, how many quarters will be left?
Note: There are 4 quarters in a dollar.
Excel in math and science
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November and December have \(30\) and \(31\) days, respectively. If November \(1\) is the first day of the week, how many days of December are there in the last week?
Excel in math and science
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How many different values are there for \( 4 ^ n \pmod { 7} \), as \(n\) ranges over all positive integers?
Excel in math and science
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What is the sum of all positive prime numbers \(x\) such that \(x^2+2\) is also a prime?
Excel in math and science
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by Brilliant Staff