Mathematics: Find a four digit number which is a perfect square. the last two digits are equal and the first two digits are equal of the number.

Find a four digit number which is a perfect square.

camillanewberry

01.01.2022

$1000x+100x+10y+y=k^2\qquad (k\in \mathbb{Z})\\
1100x+11y=k^2\\
11(100x+y)=k^2
$

11 is a prime number, so for k^2

to be a perfect square, 100x+y

must be also equal to 11. But 11^2=121

which is not even a four digit number. Therefore there is no such number.

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maciemarklin3032

09.10.2021

Yes because -2 is closer to 0 on the degree scale. The closer it is to 0 the warmer it will be(on the negative.)

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