Beginning Activity 1: Exploring Examples where \boldsymbol{a} Divides \boldsymbol{b \cdot c}

Beginning Activity Beginning Activity 1: Exploring Examples where $a$ Divides $b \cdot c$
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1.

Find at least three different examples of nonzero integers $a,$ $b,$ and $c$ such that $a ∣ (b c)$ but $a$ does not divide $b$ and $a$ does not divide $c .$ In each case, compute $gcd (a, b)$ and $gcd (a, c) .$

2.

Find at least three different examples of nonzero integers $a,$ $b,$ and $c$ such that $gcd (a, b) = 1$ and $a ∣ (b c) .$ In each example, is there any relation between the integers $a$ and $c ?$

3.

Formulate a conjecture based on your work in Exercise 1 and Exercise 2.

Mathematical Reasoning: Writing and Proof (PreTeXt Edition)

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Beginning Activity Beginning Activity 1: Exploring Examples where $a$ Divides $b \cdot c$
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Beginning Activity Beginning Activity 1: Exploring Examples where a Divides b⋅c A4US

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Beginning Activity Beginning Activity 1: Exploring Examples where $a$ Divides $b \cdot c$
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