Interesting Number 2519:

For N=2 to 10:

2519/N always gives you remainder as (N-1)

2519 / 2 gives you remainder 1

2519 / 3 gives you remainder 2

2519 / 4 gives you remainder 3

2519 / 5 gives you remainder 4

2519 / 6 gives you remainder 5

2519 / 7 gives you remainder 6

2519 / 8 gives you remainder 7

2519 / 9 gives you remainder 8

2519 / 10 gives you remainder 9

Also For N=1 to 9:

(2519-N)/(N+1) always gives you a whole number

(2519 - 1 ) / 2 = 1259

(2519 - 2 ) / 3 = 839

(2519 - 3 ) / 4 = 629

(2519 - 4 ) / 5 = 503

(2519 - 5 ) / 6 = 419

(2519 - 6 ) / 7 = 359

(2519 - 7 ) / 8 = 314

(2519 - 8 ) / 9 = 279

(2519 - 9 ) / 10 = 251

Easy Math Editor

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Comments

This is because 2520 (=2519+1) is the LCM of 1 to 10. Nice observation!

展豪張 - 5 years, 5 months ago

Good job! I notice in the second part, the whole numbers produced are mostly prime numbers, except for 629 = (17)(37), 314 = (2)(157) and 279 = (31)(3^2)

Jeganathan Sriskandarajah - 5 years, 5 months ago

Can you just add /1 because it gives remainder 0

Mohammad Farhat - 2 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}`	$\boxed{123}$