000RM.dvi
202 Greatest common divisor 5.1 gcd(a, b)as an integer combination ofaandb It is well known that the gcd of two (positive) integ ...
5.2 Nonnegative integer combinations ofaandb 203 5.2 Nonnegative integer combinations ofaandb Find thelargestpositive integer wh ...
204 Greatest common divisor 5.3 Cassini formula for Fibonacci numbers The Fibonacci numbersFnare defined recursively by Fn+1=Fn+ ...
5.4 gcd of generalized Fibonacci and Lucas numbers 205 5.4 gcd of generalized Fibonacci and Lucas numbers Givenaandb, the genera ...
206 Greatest common divisor Exercise 1.Find the gcd of the following pairs of numbers by completing the second column of each ta ...
5.4 gcd of generalized Fibonacci and Lucas numbers 207 Project Generalize 3+ 3 2 =3× 3 2 . 3+ 3 2 + 9 7 =3× 3 2 + 9 7 =3× 3 2 × ...
208 Greatest common divisor Project Write down two 1’s, then a 2 between them, then a 3 between any two numbers whose sum is 3, ...
Chapter 6 Pythagorean triples 1 Primitive Pythagorean triples 2 Primitive Pythagorean triples with square perimeter 3 Lewis Carr ...
210 Pythagorean triples 6.1 Primitive Pythagorean triples It is well known that every primitive Pythagorean triple(a, b, c)is of ...
6.2 Primitive Pythagorean triangles with square perimeters 211 6.2 Primitive Pythagorean triangles with square perime- ters Ifm& ...
212 Pythagorean triples 6.3 Lewis Carroll’s conjecture on triples of equiareal Pythagorean triangles Lewis Carroll conjectured t ...
6.4 Points at integer distances from the sides of a primitive Pythagorean triangle 213 6.4 Points at integer distances from the ...
214 Pythagorean triples 6.5 Dissecting a rectangle into Pythagorean triangles How many matches (of equal lengths) are required t ...
6.5 Dissecting a rectangle into Pythagorean triangles 215 Appendix: Primitive Pythagorean triples< 1000 m, n a, b, c m, n a, ...
216 Pythagorean triples Appendix: Dissection of a square 360 360 255 105 224 136 289 375 424 ...
6.5 Dissecting a rectangle into Pythagorean triangles 217 Exercise 1.A man has a square field, 60 feet by 60 feet, with other pr ...
218 Pythagorean triples 7.Give an example of a primitive Pythagorean triangle in which the oddleg is a square. triangle to be a ...
6.5 Dissecting a rectangle into Pythagorean triangles 219 Project: Factorablex^2 +px±q Theorem 6.1.Letpandqbe relatively prime i ...
220 Pythagorean triples Project: 64 primitive Pythagorean triangles with a common hypotenuse A product ofn+1distint prime number ...
6.5 Dissecting a rectangle into Pythagorean triangles 221 Project: Primitive Pythagorean triangles with equal perimeters perimet ...
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