Page 121 - 'Blast_Into_Math

Blast into Math! Prime nummers: indestructimle muilding mlocks

• Hint for #5: First, try examples. Start with 6, then try 7, and keep doing examples. Based on
your examples, if you think that you can write any positive integer greater than or equal to
4 as the sum of two (not necessarily distinct) primes, try proving this by induction. If you
think that it’s not true, try to find a counterexample.
√
• Hint for # 6: Try a proof by contradiction. This would mean that 2 is a rational number.
√
If 2 is a rational number, then there exist natural numbers p and q such that
√ p
2= .
q

Think about the prime factorizations of p and q using the FTA, and see what happens when
you use the definition of square root

2

p
2= .
q

• Hint for # 7: First you can look at the hint for #10 from last chapter and use it to create an
algorithm to find solutions to that problem. If you put your algorithm together with the
IMP Theorem, what does it tell you?
• Hint for # 8: What are the divisors of a prime number, which are smaller than that prime

number?

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