2002 Manhattan Mathematical Olympiad
... a) Prove that F5 is divisible by 641. (Hence Fermat was wrong.) b) Prove that if k 6= n then Fk and Fn are relatively prime (i.e. they do not have any common divisor except 1) (Notice: using b) one can prove that there are infinitely many prime numbers) ...
... a) Prove that F5 is divisible by 641. (Hence Fermat was wrong.) b) Prove that if k 6= n then Fk and Fn are relatively prime (i.e. they do not have any common divisor except 1) (Notice: using b) one can prove that there are infinitely many prime numbers) ...
2-9-1 Integer Arithmetic Review
... List the coefficient, variable and exponent of the following terms. k) 3a2 7x2y3 8.2m5 Add the following. Multiply the following. ...
... List the coefficient, variable and exponent of the following terms. k) 3a2 7x2y3 8.2m5 Add the following. Multiply the following. ...
Partial Fraction Decomposition Examples
... thereby setting up three equations in three unknowns (e.g. all coefficients of x 2 terms will sum up to 1, etc.). Method #2 (easier) is to choose any three values for x and substitute them into both sides of the equation (e.g. if x=0 then 1=6A+3B+2C) and again obtaining three equations in three unkn ...
... thereby setting up three equations in three unknowns (e.g. all coefficients of x 2 terms will sum up to 1, etc.). Method #2 (easier) is to choose any three values for x and substitute them into both sides of the equation (e.g. if x=0 then 1=6A+3B+2C) and again obtaining three equations in three unkn ...
Junior Round 2 2013 File
... Jane has three shirts, four skirts and some belts. Every combination of shirt, skirt and belt is an outfit, and Jane knows she can wear at least 50 different outfits. What is the minimum number of belts she ...
... Jane has three shirts, four skirts and some belts. Every combination of shirt, skirt and belt is an outfit, and Jane knows she can wear at least 50 different outfits. What is the minimum number of belts she ...
simplifying radical expressions
... Rationalizing the Denominator means eliminating all irrational numbers from the denominator. When eliminating a radical from a denominator, it is important that you always multiply by one – otherwise you will change the value of the fraction. Multiplying by 1 (the multiplicative identity element) d ...
... Rationalizing the Denominator means eliminating all irrational numbers from the denominator. When eliminating a radical from a denominator, it is important that you always multiply by one – otherwise you will change the value of the fraction. Multiplying by 1 (the multiplicative identity element) d ...
Elementary mathematics
Elementary mathematics consists of mathematics topics frequently taught at the primary or secondary school levels. The most basic topics in elementary mathematics are arithmetic and geometry. Beginning in the last decades of the 20th century, there has been an increased emphasis on problem solving. Elementary mathematics is used in everyday life in such activities as making change, cooking, buying and selling stock, and gambling. It is also an essential first step on the path to understanding science.In secondary school, the main topics in elementary mathematics are algebra and trigonometry. Calculus, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.