Diophantine Equations - Mastering AMC 10/12

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In this video, we will cover diophantine equations and see how we can use number theory techniques to solve them.
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For more practice, watch the AMC 10/12 Fundamentals Classes here:

If you need a refresher on the fundamentals, check out:
1. AMC 8 Fundamentals:

2. AMC 8 Advanced:

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AMC 10, AMC10, AMC 12, AMC12, AMC 10 Preparation, AMC 10 Crash Course, AMC 10 Concepts, AMC 12 Preparation, AMC 12 Crash Course, AMC 12 Concepts, AMC 10 Review, AMC 12 Review, Number Theory, Primes, Factors Competition math, number of factors, sum of factors, product of factors, AMC 10 number theory, AMC 12 number theory, diophantine equations, divisibility competition math, Area of a Triangle, Similar Triangles, Cyclic Quadrilateral, Power of a point, 3D Geo, Polygons, Coordinate Geometry, Trigonometry, Logarithms, Complex Numbers, Inequalities, Floor and Ceiling Functions, Generating Functions

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For problem 2, another solution will be to notice that (x+42)^2<x^2+84x+2008<(x+45)^2, so x^2+84x+2008 must be (x+43)^2 or (x+44)^2. Check to see that the former does not work, so 2(2x+86)=244. This gives x=18. We need 2x+44 which is 80.

thepoweroflogic

Very nice explanation! Just a trivial comment - for the 3rd question, since we only need to calculate x+y, when knowing x+y+42 = 122 is the only solution, we can directly get 80 from there.

jiangmichael

Hey sohil how comw my flexil is backwards? And how do you get your version of the book?

nathansscienceclass

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