# Math Help - Substitutions/solving equations

1. ## Substitutions/solving equations

1. Suppose that $a,b,c,d$ are real numbers such that

$a^2 + b^2 = 1$

$c^2 + d^2 = 1$

$ac+bd=0$

Show that

$a^2 + c^2 = 1$

$b^2 + d^2 = 1$

$ab + cd = 0$

(Problem can get messy but there is an elegant and complete solution)

2. Find all integer solutions $(n,m)$ to $n^4+2n^3+2n^2+2n+1=m^2$

3. Find the smallest positive integer whose cube ends in 888.

2. Originally Posted by usagi_killer
1. Suppose that $a,b,c,d$ are real numbers such that

$a^2 + b^2 = 1$

$c^2 + d^2 = 1$

$ac+bd=0$

Show that

$a^2 + c^2 = 1$

$b^2 + d^2 = 1$

$ab + cd = 0$

(Problem can get messy but there is an elegant and complete solution)

2. Find all integer solutions $(n,m)$ to $n^4+2n^3+2n^2+2n+1=m^2$

3. Find the smallest positive integer whose cube ends in 888.
Are these challenge questions?