A number theory problem by Digi Verse
Number Theory
Level
2
What is the smallest positive integer y>1 such that x and have the same units digit, when x is any positive integer?
The answer is 5.
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1 solution
The only way to approach this is by testing out the unit digit of exponents of numbers 0-9. For 0, 1, 5, and 6, you find that all their exponents are themselves, so they present no real problem. For 4 and 9, they repeat at the third power, and again at 5, and so on. For 2, 3, 7 and 8, you will find that they first repeat at the fifth power. If you line them all up, you will find that they all repeat at the fifth power, so therefore, the answer would be 5.