MathDB

The teacher calculates and writes on the board all the numbers

a^b

that satisfy the condition

n = a\times b

for the natural number

n.

Here

a

and

b

are natural numbers. Is there a natural number

n

such that each of the numbers

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

is the last digit of one of the numbers written by the teacher on the board? Justify your opinion.

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