While typing into the keyboard and staring at the screen of my old laptop, I attempted to multiply two integers, but when I checked the result by hand, the computer had given me the wrong answer.
The incorrect answer was exactly
13 times larger than the correct result. I repeated this process five more times with different pairs of integers and I continued to get a result exactly 13 times too large.
The products I should have obtained were:
14060592, 90675, 59906, 291375, 445208 and 67529.
Is there something wrong with my laptop?
I noticed: The should have list contains every digit from 0 to 9.
The prime factorizations of these have no factors in common. These don't seem to help.
Multiplying each by 13 yields a tantalizing discovery:
182787696
1178775
778778
3787875
5787704
877877
Something is causing that 787 digit string to appear in each number. (the fourth number has it twice.)
In two of the numbers if you remove the 787 string the result has a large prime factor in common with the correct product:
The 3rd number
59906=2*7*11*389
778778 becomes 778=2*389
The 6th number
67529=7*11*877
877877 becomes 877 (prime)
Am I on the right track?
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Posted by Jer
on 2022-04-22 12:51:10 |
Some thoughts
