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N000ughty Thoughts

How many noughts are at the end of these giant numbers?

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Mod 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

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Common Divisor

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.

Expenses

Age 14 to 16 Challenge Level:


What is the largest number which, when divided into each of $1905$, $2587$, $3951$, $7020$ and $8725$, leaves the same remainder each time?


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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