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Old Nuts

In turn 4 people throw away three nuts from a pile and hide a quarter of the remainder finally leaving a multiple of 4 nuts. How many nuts were at the start?

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Mod 7

Find the remainder when 3^{2001} is divided by 7.

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Remainder Hunt

What are the possible remainders when the 100-th power of an integer is divided by 125?

Purr-fection

Stage: 5 Challenge Level: Challenge Level:1

Try to be systematic. How can you narrow down the cases to be tested?

 

If the last digit of a square number is 9 what can you say about the number?

Can you write down an expression for a number using its digits and powers of 10?
Possible support

 

Note: Other problems using modulus arithmetic: Dirisibly Yours , Obviously, Rational Round
An article that explains the basic ideas of modulus arithmetic: Modulus Arithmetic and Solution to Dirisibly Yours.