number theory help this quesiton is due soon

The possible values of the tens digit are 1, 2, 4, 5, and 6.

The only numbers that can be squared to end in 6 are numbers that end in 4 or 6.

We need to find the possible values of the tens digit, so lets let the tens digit be a variable such as x.

The last two digits of our number will look like this:

10x + 6

or this:

10x + 4

I find it easiest to just plug in values from (1-9) for x and see what you get.

If x is 1, the last two digits will be ...56 or ...96

If x is 2, the last two digits will be ...76 or ...76

If x is 3, the last two digits will be ...96 or ...56

If x is 4, the last two digits will be ...16 or ...36

If x is 5, the last two digits will be ...36 or ...16

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We can keep going all the way to x=9, and you will see that the tens digit will always be an odd number...

Therefore the possible values of the tens digit is (1, 3, 5 , 7, 9)