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
Key Concepts
Smallest prime
Arithmetic Sequence
Algebra
Check the Answer
But try the problem first…
Answer: is 29.
AIME I, 1999, Question 1
Elementary Number Theory by David Burton
Try with Hints
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.
Other useful links
- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA
Related Program
AMC – AIME Boot Camp… for brilliant students.
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