Dr. Cordero
Problem #1:
- Let the three consecutive odd primes be p, p+2, p+4.
- Investigate the following question: Is it true that one of the primes p, p+2, p+4 must be divisible by 3?
- Explore the consequences of a positive answer to the question.
Problem #2:
- Write out the congruences and make conclusions about the numbers satisfying each.
- The number is less than 100.
- Your conjecture should include the number you found.
Problem # 3:
- First, find a mathematical expression which describes “the number you get when you subtract twice the 1’s digit of n from the number formed by the remaining digits of n”.
- Prove that if n is divisible by 7, then the expression you just found is divisible by 7.
- Prove that if the expression you just found is divisible by 7, then n is divisible by 7.