Does this congruence hold: 12,345,678,987,654,321 â‰¡ 0 (mod12,345,678)
I know it means it needs to be perfectly divisible, but is there anyway to figure out if it is without a calculator?
Is this a real problem? Or you made it up? :)
you can reduce it to: 987,654,321
So, it would be an integer, thus congruent, correct?
n â‰¡ 0 (mod12,345,678) doesn't this require n to be even?
The numerator is odd and the denominator is even how could it hold?
I'm not familiar with divisibility rules
no sorry @kt4rest what i meant was you could reduce the problem to: 987,654,321 â‰¡ 0 (mod12,345,678) since 12,345,678,000,000,000 is a multiple of the base but an odd number cannot be a multiple of an even number, as FFM said
The next problem in the book is asking if the congruence holds for: 12,345,678,987,654,321 â‰¡ 0 (mod12,345,679) So you may be right
That sounds correct. So, I would say this is congruent and 12,345,678,987,654,321 â‰¡ 0 (mod12,345,679) is not?
That holds the quotient is 999999999.
Thank you both