{1,4,7,10, 13, 16, 19,...}. An element of T is called irre-ducible if it is not 1 and its only factors within T are 1 and itself.3. Let T =(a) Suppose that a E T and b e T, and c is a positive integer. Provethat if a = bc, then c E T.(b) Demonstrate that every element of T can be factored as a prod-uct of irreducible elements of T.(c) Perform a sieve to find all irreducible elements of T between 1and 100.(d) Find three examples of elements of T with nonunique factoriza-tions into irreducibles.

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Asked Feb 14, 2020
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Number Theory

{1,4,7,10, 13, 16, 19,...}. An element of T is called irre-
ducible if it is not 1 and its only factors within T are 1 and itself.
3. Let T =
(a) Suppose that a E T and b e T, and c is a positive integer. Prove
that if a = bc, then c E T.
(b) Demonstrate that every element of T can be factored as a prod-
uct of irreducible elements of T.
(c) Perform a sieve to find all irreducible elements of T between 1
and 100.
(d) Find three examples of elements of T with nonunique factoriza-
tions into irreducibles.
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{1,4,7,10, 13, 16, 19,...}. An element of T is called irre- ducible if it is not 1 and its only factors within T are 1 and itself. 3. Let T = (a) Suppose that a E T and b e T, and c is a positive integer. Prove that if a = bc, then c E T. (b) Demonstrate that every element of T can be factored as a prod- uct of irreducible elements of T. (c) Perform a sieve to find all irreducible elements of T between 1 and 100. (d) Find three examples of elements of T with nonunique factoriza- tions into irreducibles.

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