Sum of digits | PRMO 2019 | Question 20

Content

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

Sum of digits - PRMO 2019

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

Key Concepts

Largest Number

Divisibility

Integer

Check the Answer

But try the problem first...

Answer: is No largest value.

Source

Try with Hints

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.

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Sum of digits | PRMO 2019 | Question 20