## October 2011 Archives

## Mon Oct 17 11:56:58 EEST 2011

### $abc$ triples

Got two lucky numbers from the math lottery.

High merit $abc$ triples related to the $abc$ conjecture $$ 11^{30}+3^{15} \cdot 13^{2} \cdot 19^{2} \cdot 41 \cdot 137 \cdot 233^{2} \cdot 44203^{2} \cdot 4758269=2^{54} \cdot 5^{8} \cdot 7^{2} \cdot 43^{4} \cdot 1451^{2} $$ $$ 2^{29} \cdot 5^{4} \cdot 7 \cdot 11^{15} \cdot 43^{2} \cdot 1451 + 13^{4} \cdot 44203^{4} \cdot 4758269^{2} = 3^{30} \cdot 19^{4} \cdot 41^{2} \cdot 137^{2} \cdot 233^{4} $$ Merits $24.2$ and $24.21$

High merit $abc$ triples related to the $abc$ conjecture $$ 11^{30}+3^{15} \cdot 13^{2} \cdot 19^{2} \cdot 41 \cdot 137 \cdot 233^{2} \cdot 44203^{2} \cdot 4758269=2^{54} \cdot 5^{8} \cdot 7^{2} \cdot 43^{4} \cdot 1451^{2} $$ $$ 2^{29} \cdot 5^{4} \cdot 7 \cdot 11^{15} \cdot 43^{2} \cdot 1451 + 13^{4} \cdot 44203^{4} \cdot 4758269^{2} = 3^{30} \cdot 19^{4} \cdot 41^{2} \cdot 137^{2} \cdot 233^{4} $$ Merits $24.2$ and $24.21$

## Wed Oct 5 12:19:32 EEST 2011

### bug stories

i got involved in a bug in a major linux distro compromising their update system if one can do "man in the middle" (e.g. DNS). the bug had strange story. i forgot to pay the internet monthly bill. the isp stopped my net, redirecting all pages to them telling me to pay. before the internet got working, i got local mail from cron about apt-key not being able to import the html page as a key. this drew my attention to the brain damaged part of apt-key. the rest of the exploit was pure triviality. another bug with a strange story was an openssl |use after free|. i was generating rsa keys with another program. imported in openssl a test key using middle clicking with the mouse. unfortunately, i have failed to select a few digits of the number, making a prime a composite (if the prime stayed prime the story would have been different). basically this broke the math. in addition openssl crashed, which was a bug. it took some time to openssl developers to realize i didn't mind the broken math but the crash. a coincidence about several other bugs is they were found while drinking coffee and smoking. no computer in the room, just relaxing. suddenly i think of something i have read today and i find it quite suspicious. leave the coffee and go to check. almost every time i wasn't wrong about the suspicion. certainly the majority of bugs were black labour (i don't think |grep -rniI stuff *| is dead, though the prevailing opinion appears different). disclaimer: this is not a tutorial :)))