This is really weird

Number Theory Level 4

Find the greatest 10-digit number, which will give a remainder of 1 when divided by 2, 3, 4, 5, 6, 7, 8, and 9 individually.

Enter 1234 if you come to the conclusion that no such number exists.

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The answer is 9999997561.

1 solution

Serkan Muhcu
Jun 28, 2016

The smallest integer divisible by $1; 2; 3; 4; 5; 6; 7; 8$ and $9$ is $5 \times 7 \times 8 \times 9 = 2520$

$10000000000 \equiv 2440 \pmod {2520}$ and therefore $10000000000 - 2439 \equiv 1 \pmod {2520}$

So the solution is $\boxed{9999997561}$

With the correct answer, pressed the wrong tab!!
Any way this is how I did it.
Smallest number divisible by 1, 2, 3, 4, 5, 6, 7, 8, and 9, N=5 7 8 9=2520. N is four digits, so the first six (biggest) must be 99999. Only the last four digits may be found. That is what we found to be added to 9999990000. 9999/2520=3.967857143.
So the integer number is 9999990000+3
2520+1=9999997561.

Niranjan Khanderia - 4 years, 10 months ago

This is really weird

Want some interesting questions like this?. Enter the world where Calculators will not help

The answer is 9999997561.

1 solution

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