 My Math Forum If f gives remainder 3 by division with 6, what remainder do 2^f^2 + 5 give?
 User Name Remember Me? Password

 Algebra Pre-Algebra and Basic Algebra Math Forum

 September 23rd, 2018, 02:17 AM #1 Member   Joined: Sep 2014 From: Sweden Posts: 94 Thanks: 0 If f gives remainder 3 by division with 6, what remainder do 2^f^2 + 5 give? If f gives remainder 3 by division with 6, what remainder do we get when we divide 2f^2 + 5 by 6? So I think I have made an attempt to solve this at least, but are not really sure if it is correct. $\displaystyle f = bq + r$ where $\displaystyle q \in \mathbb{Z}, 0 \le r< b, \ r \in \mathbb{Z}$ We have that $\displaystyle b = 6$ and $\displaystyle r = 3$. Goal: $\displaystyle 2f^2 + 5 = 6q_{1} + 5$. The goal is to write it in this form to know what remainder it gets when dividing by 6. Put in $\displaystyle f = 6q +3$ into $\displaystyle 2f^2 + 5$. Calculate LHS: $\displaystyle 2f^2 + 5 =$ $\displaystyle 2(6q+3)^{2} + 5 =$ $\displaystyle 2(6^{2}q^{2} + 2 * 3 * 6 * q + 3^{2}) + 5 =$ $\displaystyle 2 * 6^{2}q^{2} + 2 * 2 * 3 * 6 * q + 2 * 3^{2} +5 =$ $\displaystyle 6(2 * 6 * q^{2} + 2 * 2 * 3 * q + 3) + 5$ So the number within the parenthesis must be an integer. Now we have the expression on the form $\displaystyle f = 6q_{1} + r$ that was the goal. So $\displaystyle r = 5$ So this is my conclusion but to me it seems wrong because that is what is given from the beginning in the assignment. So I am not really sure this is correct. September 23rd, 2018, 04:25 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2219 Your work is correct, but can be shortened considerably. If $f = 6q + 3$, 3 divides $f$, and so 6 divides $2f^2$. Hence the remainder on dividing $2f^2 + 5$ by 6 is 5. September 23rd, 2018, 08:44 AM   #3
Member

Joined: Sep 2014
From: Sweden

Posts: 94
Thanks: 0

Quote:
 Originally Posted by skipjack Your work is correct, but can be shortened considerably. If $f = 6q + 3$, 3 divides $f$, and so 6 divides $2f^2$. Hence the remainder on dividing $2f^2 + 5$ by 6 is 5.
Well, that is what I thought,
but my school probably wants
me to stick with this method
(for now at least) for me to
show that I have understood
how it works.

Thanks for clarifying . Tags 2f2, division, give, remainder Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post deadweight Elementary Math 4 June 2nd, 2015 10:50 PM Monox D. I-Fly Algebra 9 September 17th, 2014 11:16 PM Kitty Kat Elementary Math 9 August 28th, 2014 03:12 PM listolad Algebra 1 January 12th, 2012 06:20 PM haftakhan Algebra 11 August 13th, 2011 11:22 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      