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Mathematics Talent Reward Programme (MTRP)
2024 Mathematical Talent Reward Programme
5
MTRP SUBJECTIVE Q5
MTRP SUBJECTIVE Q5
Source: MTRP 2024
March 16, 2024
algebra
Problem Statement
Let
f
:
N
⟶
N
f:\mathbb{N} \longrightarrow \mathbb{N}
f
:
N
⟶
N
such that
f
(
m
)
−
f
(
n
)
=
f
(
m
−
n
)
1
0
n
∀
m
>
n
∈
N
f(m) - f(n) = f(m-n)10^n \forall m>n \in \mathbb{N}
f
(
m
)
−
f
(
n
)
=
f
(
m
−
n
)
1
0
n
∀
m
>
n
∈
N
. Additionally, gcd
(
f
(
k
)
,
f
(
k
+
1
)
)
=
1
∀
k
∈
N
(f(k),f(k+1)) = 1 \forall k \in \mathbb{N}
(
f
(
k
)
,
f
(
k
+
1
))
=
1∀
k
∈
N
. Show that if
a
,
b
a,b
a
,
b
are coprime natural numbers, that is, gcd
(
a
,
b
)
=
1
(a,b) = 1
(
a
,
b
)
=
1
then
f
(
a
)
,
f
(
b
)
f(a),f(b)
f
(
a
)
,
f
(
b
)
are also coprime.
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