Translation into English:
For all x which are integers, there exist y and z which also are integers, such that x=5y+7z.
Is the above statement true?
Give it a few tries: triplet means (x,y,z)
(0,7,-5) is a solution
(1,10,-7) is a solution
(2,-1,1) is a solution
(3,2,-1) is a solution
(4,-2,2) is a solution
(5,-6,5) is a solution
(6,-3,3) is a solution
All other integers can therefore be obtained by adjusting values of z.
Determine whether the statement
∀x ∈ Z, ∃y, z ∈ Z[x = 5y + 7z] is true or false. Explain.
1 answer
3 answers