## Math Proofs Resources Induction proofs

Exercise 2.25: P(n) is the number of regions in the plane formed by n lines in general position: n=1, p(n)=2; n=2, p(n)=4; n=3, p(n)=7; n=4, p(n)=11; n=5, p(n)=16; n=6, p(n)=22. 2.76) Finish... Prove that for any integer z that is a perfect square, there exists integers m and n such that m^2+n^2=zk.

Let k be an integer such that there exist integers p and q with p^2+q^2=k.   Prove that for any integer z that is a perfect square, there exists integers m and n such that m^2+n^2=zk... The question is about proving limits

a) Show that if xn≠0, where n(∈) is a subset of N then lim(xn)=0 if and only if lim(1/xn2)=infinity    b) Give an example for which lim(xn)=0 but lim(1/x2n) does not exist &... prove that there does not exist n belongs to N such that n congruent 2 (mod 4) and n congruent 4 (mod 8)

prove that there does not exist n∈N such that n≡2 (mod 4) and n≡4 (mod 8). Please help this was on my last exam but I was very lost and my professor did not have enough time to go over it in class... is correct as a proof for beal conjecture?

The GCD(Ax,By) by definition divides Ax ;as a result Ax must be some multiple of GCD(Ax,By) i.e M*GCD(Ax,By) where M is some integer The GCD(Ax;By) by definition evenly divides By; As a... What is the minimum height height of a full binary tree?

What is the minimum height of a full binary tree T which has nodes n(T) = 2k-1 for k= 1, 2, ... ? fn(x)=1/(x+1/(2n)) and fn(x)=1/(x+1/(n^2)).

Q1 prove piecewise convergent on (0,infinity) Q2 prove uniform convergent on [1,infinity)   Please help with these two equations. Much Thanks, it's preparation for final exam...  Image 329k

This is page 6 of a number theory homework I worked on for a client. The assignment as a whole is a good example of some basic strategies...  Image 346k

This is page 5 of a number theory homework I worked on for a client. The assignment as a whole is a good example of some basic strategies...  Image 322k

This is page 4 of a number theory homework I worked on for a client. The assignment as a whole is a good example of some basic strategies...  Image 398k

This is page one of a number theory homework I worked on for a client. The assignment as a whole is a good example of some basic strategies...