To what number b/w 0 and 4 inclusive

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In summary, the possible range of numbers when considering 0 and 4 inclusive is 0, 1, 2, 3, and 4. Both 0 and 4 are included in the range of numbers. The difference between inclusive and exclusive is that inclusive includes both starting and ending numbers, while exclusive excludes either of them. In the range of 0 to 4 inclusive, there are 5 numbers.
  • #1
zazisr
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Q1) To what number b/w 0 and 4 inclusive is the sum 1+2+2^2+...+2^19 congruent mod 5?

Thank You.
 
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  • #2
I am reading the book What is mathematics and I am stuck on this question. If anybody could help me understand better, they would be very kind. Thankyou.
 
  • #3
One thing that might help is this:
[tex]2^0 \equiv 1 \pmod 5[/tex]
[tex]2^1 \equiv 2 \pmod 5[/tex]
[tex]2^2 \equiv -1 \pmod 5[/tex]
[tex]2^3 \equiv -2 \pmod 5[/tex]
[tex]2^4 \equiv 1 \pmod 5[/tex]
[tex]2^5 \equiv 2 \pmod 5[/tex]
[tex]2^6 \equiv -1 \pmod 5[/tex]
[tex]2^7 \equiv -2 \pmod 5[/tex]
see a pattern?

You should also know something about a nice way to simplify [tex]2^0 + 2^1 + \cdots + 2^n[/tex]
 
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  • #4
oh ok . i see now. then the answer is 0 to that.
Thank You.
 

FAQ: To what number b/w 0 and 4 inclusive

What is the possible range of numbers when considering 0 and 4 inclusive?

The possible range of numbers would be 0, 1, 2, 3, and 4.

Is 0 included in the range of numbers?

Yes, 0 is included in the range of numbers as it is mentioned in the question.

Is 4 included in the range of numbers?

Yes, 4 is included in the range of numbers as it is mentioned in the question.

What is the difference between inclusive and exclusive?

Inclusive refers to the range of numbers that includes both the starting and ending numbers, while exclusive refers to the range of numbers that excludes either the starting or ending number.

How many numbers are there in the range of 0 to 4 inclusive?

There are 5 numbers in the range of 0 to 4 inclusive: 0, 1, 2, 3, and 4.

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