Exercise · ZW-LINEAR-DIOPHANTINE-EQUATION-004 · ★☆☆ Basic
What is the greatest common divisor of \(15\) and \(35\)?
Choose one option.
Show answer
- D. \(5\)
Explanation
The common divisors of \(15\) and \(35\) are \(1\) and \(5\), so the greatest is \(5\). Choosing \(1\) ignores the shared factor, while \(7\) or \(15\) divide only one of the numbers.
Review the concept: Linear Diophantine equation
A linear Diophantine equation is \(ax+by=c\) with integer coefficients, where we seek integer pairs \(x,y\) as solutions.
\[x=x_0+\frac{b}{d}t,\quad y=y_0-\frac{a}{d}t,\quad t\in\mathbb{Z}\]
More practice problems: linear diophantine equation
- ZW-LINEAR-DIOPHANTINE-EQUATION-001 What is the greatest common divisor of 12 and 18, which determines whether 12x+18y=c has a solution?
- ZW-LINEAR-DIOPHANTINE-EQUATION-002 Which statement correctly describes when ax+by=c has integer solutions?
- ZW-LINEAR-DIOPHANTINE-EQUATION-003 What is the name of the theorem guaranteeing that d=gcd(a,b) can be written as ax+by with integers…
- ZW-LINEAR-DIOPHANTINE-EQUATION-005 Does the equation 4x+6y=5 have integer solutions?
- ZW-LINEAR-DIOPHANTINE-EQUATION-006 If 7(3)+5(-4)=1, what is a particular solution of 7x+5y=1?
- ZW-LINEAR-DIOPHANTINE-EQUATION-007 Given the particular solution (x_0,y_0)=(2,-1) of 4x+6y=2, what is the general solution with t∈ℤ?
- ZW-LINEAR-DIOPHANTINE-EQUATION-008 Let 9x+15y=12. What is the particular solution obtained from 3=9(2)+15(-1)?
- ZW-LINEAR-DIOPHANTINE-EQUATION-009 For which value of c does the equation 10x+4y=c have an integer solution?
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