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Algebra Arithmetic Math Olympiad PRMO

Sum of digits | PRMO 2019 | Question 20

Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits. You may use sequential hints to solve the problem.

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
Suggested Reading

PRMO, 2019, Question 20

Elementary Number Theory by David Burton

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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