Junior Exam J3
Each problem is worth 7 marks.
Time: 4 hours
No books, notes or calculators permitted
Note: You must answer with proof.
Let , , , and be integers such that
(a) Find the maximum value of . Find all , and which satisfy this.
(b) Find the minimum value of . Find all , and which satisfy this.
has 3 distinct integer roots which can be arranged to form an arithmetic progression. Find all and which satisfy this.
Let denote the set containing all non-zero real numbers.
(a) Find all functions such that .
(b) Find all functions such that .
Assuming , , and are positive reals:
(a) Find the value of if
(b) Prove that
is a function such that
where is a number and is a prime number. It is also known that
Find the value of