my teacher wants us to convince her that 121 is a square number no matter in what base it is written. how do i do that?

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- Oct 19th 2006, 12:24 PM #1

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- Oct 19th 2006, 02:58 PM #2

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Hello, t-lee!

My teacher wants us to convince her that 121 is a square number

no matter in what base it is written.

The number $\displaystyle 121_b$ means: .$\displaystyle 1\!\cdot\!b^2 + 2\!\cdot\!b + 1$

And we see that: .$\displaystyle b^2 + 2b + 1 \:=\:(b+1)^2$ . . . a square number.

Will that satisfy your teacher?

- Oct 19th 2006, 03:03 PM #3

- Oct 19th 2006, 03:14 PM #4

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