Prove by induction that any natural number is either even or odd…. 1 answer below »
Prove by induction that any natural number is either even or odd…. 1 answer below » | savvyessaywriters.org
(1) Prove by induction that any natural number is either even or odd.
(2) Prove by induction that 32n+1 + 2n+2 is divisible by 7 for all n ? N.
(3) Prove by induction that every natural number n = 12 can be written
as a sum of 4s and 5s.
Hint: It is useful to note that if a number greater than 12 is written
as a sum of 4s and 5s, there must be at least three terms in that
sum.
(4) Fix a natural number n. Use induction to prove that (1 + n)
3m – 1
is divisible by n for every m ? N.
Attachments:
hw1-adj.pdf
Textbook.pdf
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