Problem 2. Using modular arithmetic, find: a. the last digit of 98709090877^{20208} b. the last two digits of 99999987899999^{20204} c. the last two digits of 5678999919199^{20201} d. the last digit of 910908767073^{2030}
Added by Alberto A.
Close
Step 1
The last digit of 987090908772206: We only need to look at the last digit of the number, which is 6. Show more…
Show all steps
Your feedback will help us improve your experience
Kathleen Carty and 86 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the last two digits of 1234^5678 ( 1234^5678 mod 100 ).
Adi S.
For each integer 2 ≤ a ≤ 10, find the last four digits of a^1000. [Hint: We need to calculate a^1000 mod 10000. Use Euler's theorem and Chinese remainder theorem. For example, 10000 = 2^4 ∙ 5^4; 2^1000 ≡ 0 mod 2^4, and 2^500 ≡ 1 mod 5^4.]
How many four decimal digit positive integers (between 1000 and 9999 inclusive): Do not contain the same digit twice? End with an odd digit? Have exactly three digits that are 9s? End with an even digit?
Nick J.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD