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Questions and Answers
What does it mean if a ∤ b?
What does it mean if a ∤ b?
Which notation represents 'a divides b'?
Which notation represents 'a divides b'?
According to the Division Algorithm, what does 'a = d ×q + r' signify?
According to the Division Algorithm, what does 'a = d ×q + r' signify?
Which property states that if a | b and a | c, then a | (b + c)?
Which property states that if a | b and a | c, then a | (b + c)?
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If 4 | 64 and 8 | 64, then what can be inferred from this?
If 4 | 64 and 8 | 64, then what can be inferred from this?
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Study Notes
Divisibility Notation and Concepts
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The notation ( a \nmid b ) indicates that ( a ) does not divide ( b ) evenly, meaning there is a remainder when ( b ) is divided by ( a ).
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The notation for "a divides b" is represented as ( a \mid b ), which means that there exists an integer ( k ) such that ( b = a \times k ).
Division Algorithm
- The Division Algorithm states that for any integers ( a ) and ( d ) (where ( d > 0 )), there exist unique integers ( q ) (quotient) and ( r ) (remainder) such that ( a = d \times q + r ) with ( 0 \leq r < d ).
Properties of Divisibility
- The additive property of divisibility states that if ( a \mid b ) and ( a \mid c ), then ( a \mid (b + c) ). This means if ( a ) divides both ( b ) and ( c ), it also divides their sum.
Inference from Divisibility
- If ( 4 \mid 64 ) and ( 8 \mid 64 ), it can be inferred that both 4 and 8 divide 64 without remainder, confirming their status as divisors of 64.
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Description
Test your knowledge of number theory and its application in cryptography with this quiz. Explore concepts such as divisors, multiples, and the relationship between integers in the context of cryptographic algorithms.
