1) Prove: If 3x+5 is irrational then x is irrational. [3] 2) Prove: If a|c and b
ID: 3420957 • Letter: 1
Question
1) Prove: If 3x+5 is irrational then x is irrational. [3]
2) Prove: If a|c and b|c then ab|c^2 [3]
3) List 6 numbers congruent to 8mod5 [2]
4) Given: n,m,a,b are all integers and n and m are greater than 1. Prove that if n|m and abmod(m) then abmod(n). [3]
5) Do not use prime factorization for this problem, see other “tricks” from class. A) Explain how division can be used to determine whether or not 42 is the GCF of 840 and 882. B) Use the GCF of 840 and 882 to quickly and efficiently find the LCM of 840 and 882. Write at least one sentence explaining your work. [3]
Explanation / Answer
Do not use prime factorization for this problem, see other “tricks” from class. A) Explain how division can be used to determine whether or not 42 is the GCF of 840 and 882. B) Use the GCF of 840 and 882 to quickly and efficiently find the LCM of 840 and 882. Write at least one sentence explaining your work. [3]
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