MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2019 India IMO Training Camp
P3
P3
Part of
2019 India IMO Training Camp
Problems
(1)
NT disguised as Algebra
Source: Indian TST 2019 Practice Test 1 P3
7/17/2019
Let
n
≥
2
n\ge 2
n
≥
2
be an integer. Solve in reals:
∣
a
1
−
a
2
∣
=
2
∣
a
2
−
a
3
∣
=
3
∣
a
3
−
a
4
∣
=
⋯
=
n
∣
a
n
−
a
1
∣
.
|a_1-a_2|=2|a_2-a_3|=3|a_3-a_4|=\cdots=n|a_n-a_1|.
∣
a
1
−
a
2
∣
=
2∣
a
2
−
a
3
∣
=
3∣
a
3
−
a
4
∣
=
⋯
=
n
∣
a
n
−
a
1
∣.
algebra