Power cycle explorer

Watch the last digits of

a^k

repeat.

For checking your work after you’ve tried it yourself.

Step 1:
Type a base

Any whole number, positive or negative.

The last digit, the last two digits, or any modulus.

Type k to see where

a^k

lands in the cycle.

What it does.

Lists the last digit (or last two digits, or the remainder mod

m

) of

a, a^2, a^3, \dots

until the pattern repeats, then uses the repeat to answer for any power.

When it helps.

Checking the last digits of a big power you worked out by spotting the cycle.

What it won’t do.

It only looks at remainders, never the whole huge number.

Example.

Powers of 7 end in 7, 9, 3, 1 and then repeat.

The powers of

a

, last digit

a

What is

a^{k}

k

(optional)

a can be negative. Leave k empty to just see the cycle.

Try