Hey!
Plz guide me, what to do now?..
(with complete explanation )
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Bunti360:
What do you want me to do ? prove them that they are of some form...?
ya.. actually I am stuck in the question. Can you tell me my mistake. Also, plz tell the solution so that I can see the proper one.. And, thnx for your inquiry!
if you don't mind could you please post the actual question !. (It must contain a info, about doing a square or proving of order 5m+1 or stuff related to that)
ya sure..! : )
Show that every even positive integer is of the form 5m+1, or 5m+3 for ome odd integer m.
Answers
Answered by
1
Let a = bq+r,
Where q = 5, => 0≤r<5, and let b = m
Possibilities of r and a are,
a = 5m, if r= 0,
a = 5m+1 , if r = 1,
a = 5m+2 , if r = 2,
a = 5m+3, if r = 3,
a = 5m+4 , if r = 4,
Now, Supposing m is an odd number as per the question (Posted in the comments)
We know that,
Odd x Odd = Odd,
Odd + Odd = Even,
Odd + Even = Odd,
Here 5m is always even if m is odd,
Now all we have to do is add an odd Integer to make it even,
Which are , 1,3 in this case,
=> 5m+1 and 5m+3 are always even if m is odd,
Therefore, Hence proved that 5m+1 and 5m+3 are always even if m is odd !.
Note : You might wonder why I have done this, But remember that if the question is to prove some linear thing, Go with the question,
There is no need for doing square of these, You have to do it only when they ask "prove square of......." , If the question doesn't contain that, take q and b as what's given in the question !.
Hope you understand, Have a great day !.
Thanking you, Bunti 360 !.
Where q = 5, => 0≤r<5, and let b = m
Possibilities of r and a are,
a = 5m, if r= 0,
a = 5m+1 , if r = 1,
a = 5m+2 , if r = 2,
a = 5m+3, if r = 3,
a = 5m+4 , if r = 4,
Now, Supposing m is an odd number as per the question (Posted in the comments)
We know that,
Odd x Odd = Odd,
Odd + Odd = Even,
Odd + Even = Odd,
Here 5m is always even if m is odd,
Now all we have to do is add an odd Integer to make it even,
Which are , 1,3 in this case,
=> 5m+1 and 5m+3 are always even if m is odd,
Therefore, Hence proved that 5m+1 and 5m+3 are always even if m is odd !.
Note : You might wonder why I have done this, But remember that if the question is to prove some linear thing, Go with the question,
There is no need for doing square of these, You have to do it only when they ask "prove square of......." , If the question doesn't contain that, take q and b as what's given in the question !.
Hope you understand, Have a great day !.
Thanking you, Bunti 360 !.
Thanks a lot for help..! : )
No problem !. :D
I knew that you'll be able to solve it! Sorry for disturbance
brainly was created for this, So no disturbance, No worries !.
Yaa!!
was the solution correct as per your teacher's ?
I'll get it checked tomorrow.. : )
oh, Let me notify when you cross examine it !. :D
ya sure! ^o^
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