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Magazine Problem 1
Find the greatest common divisor of 15 and 35 .
Problem 1
Convert \((7482)_{10}\) to base 6 notation.
Problem 2
Use the division algorithm to find the quotient and the remainder when 76 is divided by 13 .
Problem 2
Find the greatest common divisor of 100 and 104 .
Problem 2
Convert \((98156)_{10}\) to base 8 notation.
Problem 2
Use the Euclidean algorithm to find the greatest common divisor of 780 and 150 and express it in terms of the two integers.
Problem 6
Show that if \(m, n \in \mathbb{Z}\) have \(\operatorname{gcd}(m, n)=1,\) then \(\operatorname{gcd}(m+n, m-n)=\) I or 2 .
Problem 7
Show that the product of two even integers is even, the product of two odd integers is odd and the product of an even integer and an odd integer is even.
