# Olympiad Math (December 7 – December 14, 2013)

Day of the Week

Today is Saturday, December 07, 2013. What day of the week $13^{2013}$ days from now will fall?

1. John Rey Jimenez. Negros Occidental High Schol

2. Arsh Singh. yourmathguru.com

3. Jomari Tan. DLSU

4. John Michael Maninang.UST

5. Raymond John Diaz. (School Please)

6. Jeffry Robles. University of the Philippines – Diliman

7. Roger Tseng

8. Marlon Chris Malicsi. UST

9. Muthu Krishnan .Kle College. Bengaluru

10. Kim Arvin P. Leocadio. Bicol University

11. Ana Quiros. DLSU.

12. Sidhhart Dwevide. IIT Bombay.

13. Quant Master. unknown. (comment your name and school pls)

14. Carl Joshua Quines, Valenzuela City Science HS

15. Carlo Jay Vizcarra. Pamantasan ng Lungsod ng Maynila

16. John Ryan Regalario (comment your school)

17. Mark C. Angeles from Unversity of Southeastern Philippines (USeP) Tagum City Campus

### 16 Responses

1. JM Maninang says:

John Michael Maninang
UST

Friday

2. Raymond John Diaz says:

Friday

3. Roger Tseng says:

Friday.Because 13 is equal to -1 modulo 7, so 13^2013 is equal to(-1)^2013=-1. One day before Saturday would be Friday.

4. friday

5. Kim Arvin P. Leocadio (Bicol University) says:

FRIDAY

6. Ana Quiros. DLSU. says:

7. Friday
13 = -1 (mod 7)
So, 13^2013 = -1 (mod 7) = 6 (mod 7)
So, it was Saturday after (13^2013 – 6) days from now.
Hence after 13^2013 days, it will be Friday.

8. Quant Master says:

FRIDAY

9. cjquines says:

Friday. Carl Joshua Quines, Valenzuela City Science HS

10. Carlo Jay Vizcarra says:

Friday

11. Carlo Jay Vizcarra says:

Pamantasan ng Lungsod ng Maynila

12. அம்பி says:

Friday

13. john ryan regalario says:

friday

14. Huzaifa Abbasi says:

Saturday

15. I’m Mark C. Angeles from Unversity of Southeastern Philippines (USeP) Tagum City Campus

16. kryptonj123 says:

The correct answer is Friday. The simplest approach is Siddharth Dwivedi’s solution.