दर्शाइए कि कोई भी धनात्मक विषम पूर्णाक 6q+1, या 6q+3, या6q+5 के रूप का होता है जहाँ q कोई पूर्णाक है।
Answers
Step-by-step explanation:
dhanatmak visham poornank = positive odd integer
ise humlog logically prove karenge
mana ki n koi bhi positive integer hai.
agar n me 6 se bhaag denge to kya kya sambhavnayen hai
1. n 6 se divide ho jayega. say n = 6x
2. n 6 se puri tarah se divide nahi hoga aur remainder yani shesh 1 bachega
i.e. n = 6x + 1
3. shesh 2 bachega. n = 6x + 2
isi tarah
4 n= 6x +3
5. n = 6x +4
6. n = 6x + 5
uprokt 1 se 6 ke alawa aur koi sambhavna nahi hai
chunki hame sirf visham poornank ke bare me baat karni hai isliye
sr no. 1 ko remove karte hai kyunki is case me 6 se divisible numbers hai jo Sam yani even number hai.
6x + 2 = 2*(3x+1) ..ye bhi Sam yani even hai
6x+4 = 2(3x+2).... ye bhi even no. hai
isliye odd number ko represent karne ke liye sirf
6x+1, 6x+3 aur 6x+5 bach
hence, any odd positive integer can be represented in the form of 6x+1, 6x+3 and 6x+5
proved