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Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Smallest prime and arithmetic sequence.

Find the smallest prime that is the fifth term of an increasing arithmetic sequence all four preceeding terms also being prime.

- is 107
- is 29
- is 840
- cannot be determined from the given information

Smallest prime

Arithmetic Sequence

Algebra

But try the problem first...

Answer: is 29.

Source

Suggested Reading

AIME I, 1999, Question 1

Elementary Number Theory by David Burton

First hint

Let the sequence be p, p+a, p+2a, p+3a, p+4a where p is prime and a is positive integer here p cannot be multiple of 2 or 3 or 4

Second Hint

then smallest p=5 taking a=6 we get a sequence of prime numbers

Final Step

5,11,17,23,29 then fifth term =29.

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

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