Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Smallest prime and arithmetic sequence.
Smallest prime Problem – AIME I, 1999
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
Check the Answer
Answer: is 29.
AIME I, 1999, Question 1
Elementary Number Theory by David Burton
Try with Hints
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
then smallest p=5 taking a=6 we get a sequence of prime numbers
5,11,17,23,29 then fifth term =29.
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