tag:blogger.com,1999:blog-2893315201359920156.post6624797390527292826..comments2023-10-28T20:35:12.856+05:30Comments on Best Brain Teasers: Math Prime number puzzle 15aprillaveshhttp://www.blogger.com/profile/03731980294342074301noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-2893315201359920156.post-91317109988423892252011-04-16T01:44:42.737+05:302011-04-16T01:44:42.737+05:30If A is even then A^2+26 is even
If A is NOT a mul...If A is even then A^2+26 is even<br />If A is NOT a multiple of 3 then A^2 is 1 Mod 3 so A^2+26 is a multiple of 3. This leaves only odd multiples of 3 as candidates of which only 3 is prime. 3^2+26=35 which is not prime.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2893315201359920156.post-52642097814903205922011-04-15T19:10:04.394+05:302011-04-15T19:10:04.394+05:30It is true.
for that consider a=2(primenumber)
sub...It is true.<br />for that consider a=2(primenumber)<br />substitute the value of a in a*a+26 then<br /> 2*2+26=4+26=30 <br />(WHICH IS NOT A PRIME)<br />Because 30=1*30<br /> 2*15<br /> 3*10<br /> 5*6<br />But A num 'a' is said to be a primenumber if it has only two multiples i.e., 1 and a onlyharipriyanoreply@blogger.comtag:blogger.com,1999:blog-2893315201359920156.post-34194732754532281032011-04-15T18:43:12.819+05:302011-04-15T18:43:12.819+05:30truetrueRathod Jigneshhttp://rathodjignesh.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-2893315201359920156.post-17746788861034517302011-04-15T17:27:44.086+05:302011-04-15T17:27:44.086+05:30Let us divide it by 3. Its a prime number, So divi...Let us divide it by 3. Its a prime number, So dividing it by 3 would result in 1 or 2 as remainder. <br /><br />If 1 is remainder and 26 is added to it. result would be 27 and it would be divisible by 3 So not a prime number. <br /><br />If 2 is remainder and 26 is added to it. result is 28 which is clearly not a prime number. <br /><br />So a * a + 26 is not a prime number.Pankaj Kumarhttps://www.blogger.com/profile/02244524719481685633noreply@blogger.comtag:blogger.com,1999:blog-2893315201359920156.post-47161309869360575072011-04-15T16:17:52.839+05:302011-04-15T16:17:52.839+05:30truetrueAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2893315201359920156.post-21835674830395290352011-04-15T14:49:04.518+05:302011-04-15T14:49:04.518+05:30True.
n=3:
3*3+26=35=5*7
n=3k+1:
(3k+1)*...True.<br />n=3: <br /> 3*3+26=35=5*7<br />n=3k+1: <br /> (3k+1)*(3k+1)+26=3*(k(3k+2)+9)<br />n=3k-1: <br /> (3k-1)*(3k-1)+26=3*(k*(3k-2)+9)techttps://www.blogger.com/profile/09529275784452561730noreply@blogger.comtag:blogger.com,1999:blog-2893315201359920156.post-80516312645786218312011-04-15T14:46:22.532+05:302011-04-15T14:46:22.532+05:30a*a + 26 = (a-2)(a+2) + 30
we can directly check ...a*a + 26 = (a-2)(a+2) + 30<br /><br />we can directly check for a equal to 3,<br /><br />a*a+26 = 35 [NOT PRIME]<br /><br />for consecutive 5 numbers scenario, consider them as below<br /><br />a-2, a-1, a, a+1, a+2<br />O1, E1, O, E2, O2<br /><br />here O=Odd, E=even<br /><br />out of O1, E1, and O<br />at least one is divisible by 3<br /><br />if O1 is divisible by 3 then (a-2)(a+2) is divisible by 3<br />if E1 is divisible by 3 then O2 is divisible by 3 and hence (a-2)(a+2) is divisible by 3<br /><br />so we can write the equation (a-2)(a+2) + 30 as<br />=> 3K + 30<br />=> 3(K+10)<br /><br />thus the number is divisible by 3 if a is not equal to 3, and hence is NOT PRIMEMysteriohttps://www.blogger.com/profile/14057348687196415547noreply@blogger.comtag:blogger.com,1999:blog-2893315201359920156.post-39356083351928590672011-04-15T14:45:02.290+05:302011-04-15T14:45:02.290+05:30This comment has been removed by the author.Mysteriohttps://www.blogger.com/profile/14057348687196415547noreply@blogger.comtag:blogger.com,1999:blog-2893315201359920156.post-8802272132941434902011-04-15T14:23:18.711+05:302011-04-15T14:23:18.711+05:30True! If 'a' is a prime number then a*a+2...True! If 'a' is a prime number then a*a+26 will not be a prime number.<br /><br />Proof: if 'a' is not a prime number then it would not be divisible by 3. After dividing by 3 it gives remainder '1' or '2' then a*a % 3 would be 1 and 1+26=27 that is divisible by 3. so "a*a+26" is not a prime number bcoz it is divisible by 3.Shubham Guptahttps://www.blogger.com/profile/17576715648516808425noreply@blogger.comtag:blogger.com,1999:blog-2893315201359920156.post-32791999170519852802011-04-15T14:15:47.761+05:302011-04-15T14:15:47.761+05:30TrueTrueAnonymousnoreply@blogger.com