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

## Comments

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TopNewestThis is because 2520 (=2519+1) is the LCM of 1 to 10. Nice observation! – 展豪 張 · 1 year, 6 months ago

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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 · 1 year, 6 months ago

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