Officials say no evidence has surfaced that he met Mr. Tsarnaev in Dagestan last year.
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In Tsarnaev's case, his parents are alive and in the Russian region of Dagestan.
It was not known whether he had spent any significant amount of time in Dagestan's capital.
She is an Avar, from one of the dozens of ethnic groups in Dagestan.
But Dagestan has gone in the opposite direction and is gripped by instability and violence.
Mr. Tsarnaev said he returned to Dagestan a year ago because he is very sick.
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"Yesterday it seemed they ate more than enough, " Dagestan nature reserve spokesman Kurban Kuniev told AP.
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Mr Aliyev's predecessor was Mr Magomedov's father, Magomedali Magomedov, who led Dagestan from 1987 to 2006.
One explanation for the differences between Tatarstan and Dagestan lies in their contrasting histories.
For now, the sole working route to Russia's Black Sea coast runs through Dagestan and Chechnya.
Mr. Magomedov, the friend from the mosque, said the bombing in Boston has puzzled people in Dagestan.
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The Tsarnaev family had lived briefly in Dagestan before moving to the United States a decade ago.
Georgian forces shot dead 11 gunmen in an operation to free hostages near the frontier with Dagestan.
His parents in Dagestan decided not to fly the remains there for burial, said family spokeswoman Heda Saratova.
Her husband, Anzor Tsarnaev, said Thursday that he expected to fly soon from Dagestan to the United States.
In 2012, his older brother spent six months with relatives in Dagestan, which has an Islamist militant insurgency.
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Asked if it was possible Tamerlan encountered Muslim fundamentalists while in Dagestan, he said there was no way.
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Then the family left Kyrgyzstan in 1999 to move to Makhachkala, the capital of Dagestan, which borders Chechnya.
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The match was played at Moscow's Luzhniki Stadium due to security concerns in Anzhi's home territory of Dagestan.
Local authorities in Dagestan say Mr. Tsarnaev, perhaps knowing he would be monitored, didn't use a mobile phone there.
Anzor Tsarnaev recently moved back to Dagestan after he and his wife divorced.
And both had traveled to Dagestan, a republic of some 3 million people.
Tsarnaeva was in Dagestan as the manhunt for her children unfolded in Boston.
Russian security services killed Abu Dujana in December during an assault on an apartment in Makhachkala, the capital of Dagestan.
His father, speaking from the Russian republic of Dagestan on Friday, said Tamerlan was religious but in a peaceful way.
For instance, Tamerlan experienced a "family crisis" when his father left his mother in 2010 and then returned home to Dagestan.
Zubeidat Tsarnaeva, the men's mother, is an Avar, the largest of the more than 30 distinct ethnic groups that comprise Dagestan.
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Law enforcement officials and family members have identified the brothers as ethnic Chechens who had lived in Dagestan, in southern Russia.
Mr Dydymov said hundreds of kilograms of fish had been bought every day by Dagestan's Nature Protection Ministry for the pelicans.
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The elder of the brothers spent several months in southern Russia last year, mostly in Dagestan but also briefly, it appears, in Chechnya itself.
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