Question

please solve this.....fasttt
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Answer 1

Answer:

4

Step-by-step explanation:

We use a topic called cyclicity here. It basically helps us find the last digits of exponents.

For eg.

2¹ = 2

2² = 4

2³ = 8

2⁴ = 16

2⁵ = 32

Here, we can see the units digit of the powers of 2 start repeating after every 4 powers, so we say that 2 has a cyclicity of 4.

For this, we only need the last digit of the given number.

2003²⁰⁰⁶ + 2004²⁰⁰⁶ + 2007²⁰⁰⁶ will have the same unit's digit as

3²⁰⁰⁶ + 4²⁰⁰⁶ + 7²⁰⁰⁶

Cyclicity of 3 = 4

Cyclicity of 4 = 2

Cyclicity of 7 = 4

2006 ÷ 4 leaves a remainder 2

2006 ÷ 2 leaves a remainder 0(Here we take 2 for ease of calculation)

3² + 4² + 7²

= 9 + 16 + 49

=Last digit 4