Hints Test #3
- 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
Write out the congruences and make conclusions about the numbers
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.