Questions asked by provedit

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• Prove that #if u# is an odd integer, then the equation #x^2+x-u=0# has no solution that is an integer?
  
• Prove that #if n# is odd, then #n=4k+1# for some #k in ZZ# or #n=4k+3# for some #k in ZZ#?
  
• Prove that for all #x,y in RR#, if #x# is rational and #y# is irrational, then #x+y# is irrational?
  
• Assume that #f_1,f_2,...,f_n,...# are the Fibonacci numbers. Then #AAn in NN, f_(4n)# is a multiple of #3#. Prove this statement is true?
  
• Prove that #(5^(2n+1)+2^(2n+1))# is divisible by #7 \ \ AA n in NN#?
  
• Derive the Formula #sum_(k=1)^nk^4=1/30(6n^5+15n^4+10n^3-n)#?
  
• Mousetrap Car-Find Average Force of Snap-Please Help?