Chinaski wrote:
forrgrav wrote:
Can someone please explain what || means? It looks like absolute value, but I though absolute value only applied when you actually put something in between the bars?
Push. Please explain the meaning of the two vertical lines || ? Never saw that in maths. It was really confusing.
Question: For the positive integers a, b, and k, a^k||b means that a^k is a divisor of b, but a^(k + 1) is not a divisor of b. If k is a positive integer and 2^k||72, then k is equal to
(A) 2
(B) 3
(C) 4
(D) 8
(E) 18
Solution: Note the first line - this is where they have DEFINED the meaning of '||' (it is not the same as modulus / absolute value in this context):
For the positive integers a, b, and k,
a^k||b means that
a^k is a divisor of b, but a^(k + 1) is not a divisor of bA possible example: 2^3 is a divisor of 24 but 2^(3+1) i.e. 2^4 is NOT a divisor of 24
Here: a = 2, k = 3 and b = 24
We have been given: 2^k||72
Here, a = 2, b = 72
This means:
2^k is a divisor of 72, but 2^(k + 1) is not a divisor of 72We know that 72 = 8 * 9 = 2^3 * 3^2
Thus, we can say for sure that:
2^3 is a divisor of 72, but 2^(3+1) is NOT a divisor of 72
[a^k is a divisor of b, but a^(k+1) is NOT a divisor of b]
Thus, k = 3
Answer B _________________
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