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Note by Yoogottam Khandelwal
2 years, 4 months ago

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This also works with 2 digit numbers where tens digit is same and the sum of unit digits is 10.

for eg,

7476=(78)_6*4

=5624 Yoogottam Khandelwal · 2 years, 4 months ago

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@Yoogottam Khandelwal Very nice observation too! Indeed both unit digits are 5, is a special case of sum of unit digits is 10. Calvin Lin Staff · 2 years, 4 months ago

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Good observation. Do you know why it works? Calvin Lin Staff · 2 years, 4 months ago

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@Calvin Lin Yes..i know..

let the number be x5 where x is any number (1,2,3..9)

but, x5 is represented numerically as 10*x+5

now, when we square x5,

(10*x+5)^2

=(100*x^2)+(2 * 5 * 10 * x)+25

=(100 * x^2)+(100 * x)+25

=100(x^2+x)+25

=100 * x * (x+1)+25

so, the square of x5 is x * (x+1)_25 Yoogottam Khandelwal · 2 years, 4 months ago

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