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Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits.

Consider the set E of all natural numbers n such that when divided by 11,12,13 respectively, the remainders, in that order, are distinct prime numbers in an arithmetic progression. If N is the largest number in E, find the sum of digits of N.

- is 107
- is No largest value
- is 840
- cannot be determined from the given information

Largest Number

Divisibility

Integer

But try the problem first...

Answer: is No largest value.

Source

Suggested Reading

PRMO, 2019, Question 20

Elementary Number Theory by David Burton

First hint

here N can be of the form (13)(12)(11)(k)+29

Second Hint

where k belongs to an integer

Final Step

then no largest value.

- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA

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