Interesting Reverse Relation under square between 12,&,21

by adityaguharoy, Jul 5, 2017, 11:26 AM

Note that 12 and 21 are reverse numbers of each other.
And also,
$12^2=144$ and $21^2=441$ which are again reverse numbers of each other !!
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interesting

by dipdas, Jul 9, 2017, 2:35 PM

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If square is a three digit number then Let $x>y, (10x+y)^2=100a+10b+c and (10y+x)^2=100c+10b+a$
Now we subtract this two equation and we get $x^2-y^2=a-c\\ a-c\le 8$
So $x^2-y^2\le 8$ here $x<4$ and as $x>y so x\ne 1$
now $y=1\Rightarrow x^2\le 9$ so $x=2,3$
Again $y=2\Rightarrow x^2\le 12$ so $x=2,3$
so pairs are $(12,21) and (13,31)$
But their are infinite examples in this type you can see here Click to reveal hidden text

by Vimath, Aug 23, 2017, 8:51 PM

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