Elementary Abstract Algebra- Examples and Applications, 2019a

136 CHAPTER 3 MODULAR ARITHMETIC
}
{
//’%’ returns the remainder of the integer division
remainder = b % a;
if (remainder == 0)
return a;
else
return gcdRecurse(a, remainder);
}
else
{
remainder = a % b;
if (remainder == 0)
return b;
else
return gcdRecurse(b, remainder);
}
//By calling itself, it will repeat the process until the remainder is 0
Exercise 3.5.9. Create a spreadsheet (with Excel, LibreOffice, or OpenOffice)
that calculates the gcd of two integers that uses the procedure above.
Excel has a built-in gcd function, but you’re not allowed to use it for this exercise.But
you may use the MOD function: “=MOD(A2,B2)” will compute
the remainder when A2 is divided by B2. You may refer to the spreadsheet
in Figure 3.5.8 for ideas.
♦
3.5.4 Diophantine equations
Let’s look now at another type of problem, which has played a key role in
the history of mathematics.
Definition 3.5.10. A Diophantine equation in the variables m, n is an
equation of the form
a · m + b · n = c
where a, b, c are integers, and m and n are assumed to have integer values.
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