Math-Magic Generalized Fermat Numbers

S., Yathiraj (2023) Math-Magic Generalized Fermat Numbers. At Right Angles. pp. 52-55. ISSN 2582-1873

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Abstract

Some of you might have come across the following ‘Magic’ of numbers. Take a three-digit number, say 123. Repeat the same sequence of digits to make a six-digit number (in our case 123123). Now divide this by 7. To your surprise you get an integer again, i.e., 7 completely divides 123123 (in our case we get the quotient 17589). Next, divide the quotient by 11. Again, to your surprise, the resulting number is an integer (in our case, 1599). Finally, divide the new quotient by 13. Magic! You get back 123, i.e., you have extracted the original number. Oh! Is it really magic? I mean, does it work for all three-digit numbers? Readers may stop at this point to explore whether the magic holds for other such numbers (say 516516). Not just that, readers may try to find out whether this ‘magic’ works for all six-digit numbers. (For instance, does it work for 237765?)

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Articles in APF Magazines

Authors:

S., Yathiraj

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