1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Modular Arithmetic and Congruence Modulo
Show that eve...
Question
Show that every positive integer is either even or odd..
Open in App
Solution
Let
I
be a positive integer
We can now write
I
in the from of
I
=
p
q
+
r
So,
p
q
+
r
can either be even or odd.
Since,
p
q
+
r
yields either even or odd number
⇒
if
p
q
+
r
is even
p
q
+
r
=
2
x
and if odd
p
q
+
r
=
2
x
+
1
So,
I
=
2
x
or
2
x
+
1
⇒
I
=
odd or even
Suggest Corrections
1
Similar questions
Q.
Show that any positive integer is either even or odd.
Q.
Show that every even positive integer is in the form 5m+1 or 5m+3 for some odd integer m
Q.
Show that every positive even integer is of the form
2
n
and every positive odd integer is of the form
2
n
+
1
.
Q.
Show that every positive even integer is of the form 2q, and that every positive odd integer is of the form 2q + 1, where q is some integer.
Q.
Show that every positive even integer is of the form
2
q
and that every positive odd integer is of the form
2
q
+
1
, where
q
is an integer.
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Passage 22
MATHEMATICS
Watch in App
Explore more
Modular Arithmetic and Congruence Modulo
Standard X Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app