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# Number Theory

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How many 6-digit numbers have the property that the sum of the first 3 digits = the sum of the last 3 digits and that it is a multiple of 1009? Thank you for help.

Jan 26, 2020

#1
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I think this is a computer coding assignment. Because there are 900,000 numbers to be checked !! Even if you were to narrow it down to just the multiples of 1009, you would still have almost 900 numbers to check !!.

Jan 26, 2020
#2
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I agree with the above Guest #1. This is a job for a computer code. I wrote a short code and it gives the following result:

116035  125116  161440  170521  188683  197764  232070  241151  250232  268394  277475  286556  295637  357186  366267  375348  384429  429834  438915  455059  491383  509545  518626  527707  554950  571094  580175  607418  625580  634661  643742  652823  661904  705291  714372  723453  732534  741615  759777  768858  777939  803164  812245  821326  830407  839488  848569  884893  893974  901037  910118  919199  973685  982766  991847  Total =  55 such numbers

Jan 27, 2020