Perplexing Sum Of Remainders

May anyone kindly help me solve the following problem:

N is a 4-digit number with the property that it is made up of four consecutive integers which are in decreasing order when read from left to right. Find the sum of all the possible remainders when N is divided by 37.

I would be grateful to anyone who can show me how to solve this problem.

Thank You in advance.

#NumberTheory

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

Why can't you just list out all the 12 integers, and find their respective remainders when divided by 37?

Pi Han Goh - 3 years, 10 months ago

Oh, I never thought about that. Thank you very much. But, I don't get why there are 12 integers. Shouldn't there be just 7?

Nilabha Saha - 3 years, 10 months ago

Oh sorry, yes, just 7.

Pi Han Goh - 3 years, 10 months ago

@Pi Han Goh – Anyway, thanks a lot. :)

Nilabha Saha - 3 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$